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@article{adamo_1999a,
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title = {Toward Reliable Density Functional Methods without Adjustable Parameters: {{The PBE0}} Model},
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shorttitle = {Toward Reliable Density Functional Methods without Adjustable Parameters},
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author = {Adamo, Carlo and Barone, Vincenzo},
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year = {1999},
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month = apr,
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journal = {J. Chem. Phys.},
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volume = {110},
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number = {13},
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pages = {6158--6170},
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publisher = {{American Institute of Physics}},
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issn = {0021-9606},
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doi = {10.1063/1.478522},
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file = {/Users/monino/Zotero/storage/EHYRIT8T/Adamo et Barone - 1999 - Toward reliable density functional methods without.pdf}
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}
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@article{andersson_1990,
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title = {Second-Order Perturbation Theory with a {{CASSCF}} Reference Function},
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author = {Andersson, Kerstin. and Malmqvist, Per Aake. and Roos, Bjoern O. and Sadlej, Andrzej J. and Wolinski, Krzysztof.},
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@ -129,6 +145,35 @@
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file = {/Users/monino/Zotero/storage/W9FBB4VK/00268976.2016.html}
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}
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@article{becke_1988b,
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title = {Density-Functional Exchange-Energy Approximation with Correct Asymptotic Behavior},
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author = {Becke, A. D.},
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year = {1988},
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month = sep,
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journal = {Phys. Rev. A},
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volume = {38},
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number = {6},
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pages = {3098--3100},
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publisher = {{American Physical Society}},
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doi = {10.1103/PhysRevA.38.3098},
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abstract = {Current gradient-corrected density-functional approximations for the exchange energies of atomic and molecular systems fail to reproduce the correct 1/r asymptotic behavior of the exchange-energy density. Here we report a gradient-corrected exchange-energy functional with the proper asymptotic limit. Our functional, containing only one parameter, fits the exact Hartree-Fock exchange energies of a wide variety of atomic systems with remarkable accuracy, surpassing the performance of previous functionals containing two parameters or more., This article appears in the following collection:},
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file = {/Users/monino/Zotero/storage/HYTWLA6W/Becke - 1988 - Density-functional exchange-energy approximation w.pdf;/Users/monino/Zotero/storage/8JN8MYC2/PhysRevA.38.html}
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}
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@article{becke_1993b,
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title = {Density-functional Thermochemistry. {{III}}. {{The}} Role of Exact Exchange},
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author = {Becke, Axel D.},
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year = {1993},
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month = apr,
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journal = {J. Chem. Phys.},
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volume = {98},
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number = {7},
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pages = {5648--5652},
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publisher = {{American Institute of Physics}},
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issn = {0021-9606},
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doi = {10.1063/1.464913}
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}
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@article{casanova_2020,
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title = {Spin-Flip Methods in Quantum Chemistry},
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author = {Casanova, David and Krylov, Anna I.},
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@ -160,6 +205,20 @@
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doi = {10.1063/1.470315}
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}
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@article{dunning_1989,
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title = {Gaussian Basis Sets for Use in Correlated Molecular Calculations. {{I}}. {{The}} Atoms Boron through Neon and Hydrogen},
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author = {Dunning, Thom H.},
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year = {1989},
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month = jan,
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journal = {J. Chem. Phys.},
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volume = {90},
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number = {2},
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pages = {1007--1023},
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publisher = {{American Institute of Physics}},
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issn = {0021-9606},
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doi = {10.1063/1.456153}
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}
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@article{eckert-maksic_2006,
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title = {Automerization Reaction of Cyclobutadiene and Its Barrier Height: {{An}} Ab Initio Benchmark Multireference Average-Quadratic Coupled Cluster Study},
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shorttitle = {Automerization Reaction of Cyclobutadiene and Its Barrier Height},
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@ -193,6 +252,21 @@
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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}
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}
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@article{ernzerhof_1999,
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title = {Assessment of the {{Perdew}}\textendash{{Burke}}\textendash{{Ernzerhof}} Exchange-Correlation Functional},
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author = {Ernzerhof, Matthias and Scuseria, Gustavo E.},
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year = {1999},
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month = mar,
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journal = {J. Chem. Phys.},
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volume = {110},
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number = {11},
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pages = {5029--5036},
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publisher = {{American Institute of Physics}},
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issn = {0021-9606},
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doi = {10.1063/1.478401},
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file = {/Users/monino/Zotero/storage/KI5Z4SJW/Ernzerhof et Scuseria - 1999 - Assessment of the Perdew–Burke–Ernzerhof exchange-.pdf}
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}
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@article{fantuzzi_2016,
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title = {The {{Nature}} of the {{Singlet}} and {{Triplet States}} of {{Cyclobutadiene}} as {{Revealed}} by {{Quantum Interference}}},
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author = {Fantuzzi, Felipe and Cardozo, Thiago M. and Nascimento, Marco A. C.},
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@ -209,6 +283,23 @@
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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}
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}
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@article{garniron_2019,
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title = {Quantum {{Package}} 2.0: {{An Open-Source Determinant-Driven Suite}} of {{Programs}}},
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shorttitle = {Quantum {{Package}} 2.0},
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author = {Garniron, Yann and Applencourt, Thomas and Gasperich, Kevin and Benali, Anouar and Fert{\'e}, Anthony and Paquier, Julien and Pradines, Barth{\'e}l{\'e}my and Assaraf, Roland and Reinhardt, Peter and Toulouse, Julien and Barbaresco, Pierrette and Renon, Nicolas and David, Gr{\'e}goire and Malrieu, Jean-Paul and V{\'e}ril, Micka{\"e}l and Caffarel, Michel and Loos, Pierre-Fran{\c c}ois and Giner, Emmanuel and Scemama, Anthony},
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year = {2019},
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month = jun,
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journal = {J. Chem. Theory Comput.},
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volume = {15},
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number = {6},
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pages = {3591--3609},
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publisher = {{American Chemical Society}},
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issn = {1549-9618},
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doi = {10.1021/acs.jctc.9b00176},
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abstract = {Quantum chemistry is a discipline which relies heavily on very expensive numerical computations. The scaling of correlated wave function methods lies, in their standard implementation, between O(N5) and O(eN), where N is proportional to the system size. Therefore, performing accurate calculations on chemically meaningful systems requires (i) approximations that can lower the computational scaling and (ii) efficient implementations that take advantage of modern massively parallel architectures. Quantum Package is an open-source programming environment for quantum chemistry specially designed for wave function methods. Its main goal is the development of determinant-driven selected configuration interaction (sCI) methods and multireference second-order perturbation theory (PT2). The determinant-driven framework allows the programmer to include any arbitrary set of determinants in the reference space, hence providing greater methodological freedom. The sCI method implemented in Quantum Package is based on the CIPSI (Configuration Interaction using a Perturbative Selection made Iteratively) algorithm which complements the variational sCI energy with a PT2 correction. Additional external plugins have been recently added to perform calculations with multireference coupled cluster theory and range-separated density-functional theory. All the programs are developed with the IRPF90 code generator, which simplifies collaborative work and the development of new features. Quantum Package strives to allow easy implementation and experimentation of new methods, while making parallel computation as simple and efficient as possible on modern supercomputer architectures. Currently, the code enables, routinely, to realize runs on roughly 2 000 CPU cores, with tens of millions of determinants in the reference space. Moreover, we have been able to push up to 12 288 cores in order to test its parallel efficiency. In the present manuscript, we also introduce some key new developments: (i) a renormalized second-order perturbative correction for efficient extrapolation to the full CI limit and (ii) a stochastic version of the CIPSI selection performed simultaneously to the PT2 calculation at no extra cost.},
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file = {/Users/monino/Zotero/storage/I2Q5L62K/Garniron et al. - 2019 - Quantum Package 2.0 An Open-Source Determinant-Dr.pdf}
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}
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@article{hirata_2000,
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title = {High-Order Determinantal Equation-of-Motion Coupled-Cluster Calculations for Electronic Excited States},
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author = {Hirata, So and Nooijen, Marcel and Bartlett, Rodney J.},
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@ -351,6 +442,21 @@
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file = {/Users/monino/Zotero/storage/L3VLAU8A/Kucharski et Bartlett - 1991 - Recursive intermediate factorization and complete .pdf}
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}
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@article{lee_1988a,
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title = {Development of the {{Colle-Salvetti}} Correlation-Energy Formula into a Functional of the Electron Density},
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author = {Lee, Chengteh and Yang, Weitao and Parr, Robert G.},
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year = {1988},
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month = jan,
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journal = {Phys. Rev. B},
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volume = {37},
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number = {2},
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pages = {785--789},
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publisher = {{American Physical Society}},
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doi = {10.1103/PhysRevB.37.785},
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abstract = {A correlation-energy formula due to Colle and Salvetti [Theor. Chim. Acta 37, 329 (1975)], in which the correlation energy density is expressed in terms of the electron density and a Laplacian of the second-order Hartree-Fock density matrix, is restated as a formula involving the density and local kinetic-energy density. On insertion of gradient expansions for the local kinetic-energy density, density-functional formulas for the correlation energy and correlation potential are then obtained. Through numerical calculations on a number of atoms, positive ions, and molecules, of both open- and closed-shell type, it is demonstrated that these formulas, like the original Colle-Salvetti formulas, give correlation energies within a few percent., This article appears in the following collection:},
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file = {/Users/monino/Zotero/storage/HXKK4EQ3/Lee et al. - 1988 - Development of the Colle-Salvetti correlation-ener.pdf;/Users/monino/Zotero/storage/CCMCH9PM/PhysRevB.37.html}
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}
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@article{lefrancois_2015,
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title = {Adapting Algebraic Diagrammatic Construction Schemes for the Polarization Propagator to Problems with Multi-Reference Electronic Ground States Exploiting the Spin-Flip Ansatz},
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author = {Lefrancois, Daniel and Wormit, Michael and Dreuw, Andreas},
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@ -472,6 +578,21 @@
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file = {/Users/monino/Zotero/storage/HGW4QMJY/Aromaticity+and+Antiaromaticity+Electronic+and+Structural+Aspects-p-9780471593829.html}
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}
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@article{peverati_2011,
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title = {Improving the {{Accuracy}} of {{Hybrid Meta-GGA Density Functionals}} by {{Range Separation}}},
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author = {Peverati, Roberto and Truhlar, Donald G.},
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year = {2011},
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month = nov,
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journal = {J. Phys. Chem. Lett.},
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volume = {2},
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number = {21},
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pages = {2810--2817},
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publisher = {{American Chemical Society}},
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doi = {10.1021/jz201170d},
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abstract = {The Minnesota family of exchange\textendash correlation functionals, which consists of meta generalized gradient approximations (meta-GGAs) and global-hybrid meta-GGAs, has been successful for density functional calculations of molecular structure, properties, and thermochemistry, kinetics, noncovalent interactions, and spectroscopy. Here, we generalize the functional form by using range-separated hybrid meta-GGA exchange. We optimize a functional, called M11, with the new form against a broad database of energetic chemical properties and compare its performance to that of several other functionals, including previous Minnesota functionals. We require the percentage of Hartree\textendash Fock exchange to be 100 at large interelectronic distance, and we find an optimum percentage of 42.8 at short range. M11 has good across-the-board performance and the smallest mean unsigned error over the whole test set of 332 data; it has especially good performance for main-group atomization energies, proton affinities, electron affinities, alkyl bond dissociation energies, barrier heights, noncovalent interaction energies, and charge-transfer electronic excitation.},
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file = {/Users/monino/Zotero/storage/PSFGYXNN/Peverati et Truhlar - 2011 - Improving the Accuracy of Hybrid Meta-GGA Density .pdf;/Users/monino/Zotero/storage/FB9CZB9Y/jz201170d.html}
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}
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@article{qu_2015,
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title = {Photoisomerization of {{Silyl-Substituted Cyclobutadiene Induced}} by {$\sigma~\rightarrow$} {$\pi$}* {{Excitation}}: {{A Computational Study}}},
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shorttitle = {Photoisomerization of {{Silyl-Substituted Cyclobutadiene Induced}} by {$\sigma~\rightarrow$} {$\pi$}* {{Excitation}}},
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@ -537,6 +658,23 @@
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file = {/Users/monino/Zotero/storage/EEIUEQUN/Schoonmaker et al. - 2018 - Quantum mechanical tunneling in the automerization.pdf}
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}
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@article{shao_2015,
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title = {Advances in Molecular Quantum Chemistry Contained in the {{Q-Chem}} 4 Program Package},
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author = {Shao, Yihan and Gan, Zhengting and Epifanovsky, Evgeny and Gilbert, Andrew T.B. and Wormit, Michael and Kussmann, Joerg and Lange, Adrian W. and Behn, Andrew and Deng, Jia and Feng, Xintian and Ghosh, Debashree and Goldey, Matthew and Horn, Paul R. and Jacobson, Leif D. and Kaliman, Ilya and Khaliullin, Rustam Z. and Ku{\'s}, Tomasz and Landau, Arie and Liu, Jie and Proynov, Emil I. and Rhee, Young Min and Richard, Ryan M. and Rohrdanz, Mary A. and Steele, Ryan P. and Sundstrom, Eric J. and Woodcock, H. Lee and Zimmerman, Paul M. and Zuev, Dmitry and Albrecht, Ben and Alguire, Ethan and Austin, Brian and Beran, Gregory J. O. and Bernard, Yves A. and Berquist, Eric and Brandhorst, Kai and Bravaya, Ksenia B. and Brown, Shawn T. and Casanova, David and Chang, Chun-Min and Chen, Yunqing and Chien, Siu Hung and Closser, Kristina D. and Crittenden, Deborah L. and Diedenhofen, Michael and DiStasio, Robert A. and Do, Hainam and Dutoi, Anthony D. and Edgar, Richard G. and Fatehi, Shervin and {Fusti-Molnar}, Laszlo and Ghysels, An and {Golubeva-Zadorozhnaya}, Anna and Gomes, Joseph and {Hanson-Heine}, Magnus W.D. and Harbach, Philipp H.P. and Hauser, Andreas W. and Hohenstein, Edward G. and Holden, Zachary C. and Jagau, Thomas-C. and Ji, Hyunjun and Kaduk, Benjamin and Khistyaev, Kirill and Kim, Jaehoon and Kim, Jihan and King, Rollin A. and Klunzinger, Phil and Kosenkov, Dmytro and Kowalczyk, Tim and Krauter, Caroline M. and Lao, Ka Un and Laurent, Ad{\`e}le D. and Lawler, Keith V. and Levchenko, Sergey V. and Lin, Ching Yeh and Liu, Fenglai and Livshits, Ester and Lochan, Rohini C. and Luenser, Arne and Manohar, Prashant and Manzer, Samuel F. and Mao, Shan-Ping and Mardirossian, Narbe and Marenich, Aleksandr V. and Maurer, Simon A. and Mayhall, Nicholas J. and Neuscamman, Eric and Oana, C. Melania and {Olivares-Amaya}, Roberto and O'Neill, Darragh P. and Parkhill, John A. and Perrine, Trilisa M. and Peverati, Roberto and Prociuk, Alexander and Rehn, Dirk R. and Rosta, Edina and Russ, Nicholas J. and Sharada, Shaama M. and Sharma, Sandeep and Small, David W. and Sodt, Alexander and Stein, Tamar and St{\"u}ck, David and Su, Yu-Chuan and Thom, Alex J.W. and Tsuchimochi, Takashi and Vanovschi, Vitalii and Vogt, Leslie and Vydrov, Oleg and Wang, Tao and Watson, Mark A. and Wenzel, Jan and White, Alec and Williams, Christopher F. and Yang, Jun and Yeganeh, Sina and Yost, Shane R. and You, Zhi-Qiang and Zhang, Igor Ying and Zhang, Xing and Zhao, Yan and Brooks, Bernard R. and Chan, Garnet K.L. and Chipman, Daniel M. and Cramer, Christopher J. and Goddard, William A. and Gordon, Mark S. and Hehre, Warren J. and Klamt, Andreas and Schaefer, Henry F. and Schmidt, Michael W. and Sherrill, C. David and Truhlar, Donald G. and Warshel, Arieh and Xu, Xin and {Aspuru-Guzik}, Al{\'a}n and Baer, Roi and Bell, Alexis T. and Besley, Nicholas A. and Chai, Jeng-Da and Dreuw, Andreas and Dunietz, Barry D. and Furlani, Thomas R. and Gwaltney, Steven R. and Hsu, Chao-Ping and Jung, Yousung and Kong, Jing and Lambrecht, Daniel S. and Liang, WanZhen and Ochsenfeld, Christian and Rassolov, Vitaly A. and Slipchenko, Lyudmila V. and Subotnik, Joseph E. and Van Voorhis, Troy and Herbert, John M. and Krylov, Anna I. and Gill, Peter M.W. and {Head-Gordon}, Martin},
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year = {2015},
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month = jan,
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journal = {Mol. Phys.},
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volume = {113},
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number = {2},
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pages = {184--215},
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publisher = {{Taylor \& Francis}},
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issn = {0026-8976},
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doi = {10.1080/00268976.2014.952696},
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abstract = {A summary of the technical advances that are incorporated in the fourth major release of the Q-Chem quantum chemistry program is provided, covering approximately the last seven years. These include developments in density functional theory methods and algorithms, nuclear magnetic resonance (NMR) property evaluation, coupled cluster and perturbation theories, methods for electronically excited and open-shell species, tools for treating extended environments, algorithms for walking on potential surfaces, analysis tools, energy and electron transfer modelling, parallel computing capabilities, and graphical user interfaces. In addition, a selection of example case studies that illustrate these capabilities is given. These include extensive benchmarks of the comparative accuracy of modern density functionals for bonded and non-bonded interactions, tests of attenuated second order M\o ller\textendash Plesset (MP2) methods for intermolecular interactions, a variety of parallel performance benchmarks, and tests of the accuracy of implicit solvation models. Some specific chemical examples include calculations on the strongly correlated Cr2 dimer, exploring zeolite-catalysed ethane dehydrogenation, energy decomposition analysis of a charged ter-molecular complex arising from glycerol photoionisation, and natural transition orbitals for a Frenkel exciton state in a nine-unit model of a self-assembling nanotube.},
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annotation = {\_eprint: https://doi.org/10.1080/00268976.2014.952696},
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file = {/Users/monino/Zotero/storage/WKMD4DBC/Shao et al. - 2015 - Advances in molecular quantum chemistry contained .pdf;/Users/monino/Zotero/storage/TBGBBMR4/00268976.2014.html}
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}
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@article{shen_2012,
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title = {Combining Active-Space Coupled-Cluster Methods with Moment Energy Corrections via the {{CC}}({{P}};{{Q}}) Methodology, with Benchmark Calculations for Biradical Transition States},
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author = {Shen, Jun and Piecuch, Piotr},
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@ -632,4 +770,37 @@
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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}
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}
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@article{yanai_2004a,
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title = {A New Hybrid Exchange\textendash Correlation Functional Using the {{Coulomb-attenuating}} Method ({{CAM-B3LYP}})},
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author = {Yanai, Takeshi and Tew, David P and Handy, Nicholas C},
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year = {2004},
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month = jul,
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journal = {Chemical Physics Letters},
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volume = {393},
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number = {1},
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pages = {51--57},
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issn = {0009-2614},
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doi = {10.1016/j.cplett.2004.06.011},
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abstract = {A new hybrid exchange\textendash correlation functional named CAM-B3LYP is proposed. It combines the hybrid qualities of B3LYP and the long-range correction presented by Tawada et al. [J. Chem. Phys., in press]. We demonstrate that CAM-B3LYP yields atomization energies of similar quality to those from B3LYP, while also performing well for charge transfer excitations in a dipeptide model, which B3LYP underestimates enormously. The CAM-B3LYP functional comprises of 0.19 Hartree\textendash Fock (HF) plus 0.81 Becke 1988 (B88) exchange interaction at short-range, and 0.65 HF plus 0.35 B88 at long-range. The intermediate region is smoothly described through the standard error function with parameter 0.33.},
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langid = {english},
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file = {/Users/monino/Zotero/storage/85SV7MII/Yanai et al. - 2004 - A new hybrid exchange–correlation functional using.pdf;/Users/monino/Zotero/storage/N5PL4H9N/S0009261404008620.html}
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||||
}
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||||
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@article{zhao_2008,
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title = {The {{M06}} Suite of Density Functionals for Main Group Thermochemistry, Thermochemical Kinetics, Noncovalent Interactions, Excited States, and Transition Elements: Two New Functionals and Systematic Testing of Four {{M06-class}} Functionals and 12 Other Functionals},
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shorttitle = {The {{M06}} Suite of Density Functionals for Main Group Thermochemistry, Thermochemical Kinetics, Noncovalent Interactions, Excited States, and Transition Elements},
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author = {Zhao, Yan and Truhlar, Donald G.},
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year = {2008},
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month = may,
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journal = {Theor Chem Account},
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volume = {120},
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number = {1},
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pages = {215--241},
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issn = {1432-2234},
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doi = {10.1007/s00214-007-0310-x},
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abstract = {We present two new hybrid meta exchange- correlation functionals, called M06 and M06-2X. The M06 functional is parametrized including both transition metals and nonmetals, whereas the M06-2X functional is a high-nonlocality functional with double the amount of nonlocal exchange (2X), and it is parametrized only for nonmetals.The functionals, along with the previously published M06-L local functional and the M06-HF full-Hartree\textendash Fock functionals, constitute the M06 suite of complementary functionals. We assess these four functionals by comparing their performance to that of 12 other functionals and Hartree\textendash Fock theory for 403 energetic data in 29 diverse databases, including ten databases for thermochemistry, four databases for kinetics, eight databases for noncovalent interactions, three databases for transition metal bonding, one database for metal atom excitation energies, and three databases for molecular excitation energies. We also illustrate the performance of these 17 methods for three databases containing 40 bond lengths and for databases containing 38 vibrational frequencies and 15 vibrational zero point energies. We recommend the M06-2X functional for applications involving main-group thermochemistry, kinetics, noncovalent interactions, and electronic excitation energies to valence and Rydberg states. We recommend the M06 functional for application in organometallic and inorganometallic chemistry and for noncovalent interactions.},
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langid = {english},
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file = {/Users/monino/Zotero/storage/9VH8QARI/Zhao et Truhlar - 2008 - The M06 suite of density functionals for main grou.pdf}
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}
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@ -211,7 +211,7 @@
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\affiliation{\LCPQ}
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\begin{abstract}
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The cyclobutadiene (CBD) molecule represents a playground for ground state and excited states methods. Indeed due to the high symmetry of the molecule, especially at the square geometry ($D_{4h}$), the ground state and the excited states of the CBD exhibit multiconfigurational character where single reference methods such as adiabatic time-dependent density functional theory (TD-DFT) or equation-of-motion coupled cluster (EOM-CC) show difficulty to describe them. In this work we provide an extensive study of the autoisomerization barrier (AB), where the rectangular ($D_{2h}$) and the square geometry ($D_{4h}$) are needed, and of the vertical excitations energies of the CBD molecule using a large range of methods and basis set. In order to tackle the problem of multiconfigurational character presents in the AB and in the vertical excitation energies selected configuration interaction (sCI) and multi reference (CASSCF,CASPT2,NEVPT2) calculations are performed. Moreover coupled cluster calculations such as CCSD, CC3, CCSDT, CC4 and CCSDTQ are added to the set of methods. To complete the study we provide spin-flip (SF) results, which are known to give correct description of multiconfigurational character states, in the TD-DFT framework where numerous exchange-correlation functionals are considered, we also add algebraic diagrammatic construction (ADC) calculations in the SF formalism where we use the ADC(2)-s, ADC(2)-x and ADC(3) schemes. A theoretical best estimate (TBE) is given for the AB and for each vertical energies.
|
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The cyclobutadiene (CBD) molecule represents a playground for ground state and excited states methods. Indeed due to the high symmetry of the molecule, especially at the square geometry ($D_{4h}$) but also at the rectangular structure ($D_{2h}$), the ground state and the excited states of the CBD exhibit multiconfigurational character where single reference methods such as adiabatic time-dependent density functional theory (TD-DFT) or equation-of-motion coupled cluster (EOM-CC) show difficulty to describe them. In this work we provide an extensive study of the autoisomerization barrier (AB), where the rectangular ($D_{2h}$) and the square geometry ($D_{4h}$) are needed, and of the vertical excitations energies of the CBD molecule using a large range of methods and basis set. In order to tackle the problem of multiconfigurational character presents in the AB and in the vertical excitation energies selected configuration interaction (SCI) and multi reference (CASSCF,CASPT2,NEVPT2) calculations are performed. Moreover coupled cluster calculations such as CCSD, CC3, CCSDT, CC4 and CCSDTQ are added to the set of methods. To complete the study we provide spin-flip (SF) results, which are known to give correct description of multiconfigurational character states, in the TD-DFT framework where numerous exchange-correlation functionals are considered, we also add algebraic diagrammatic construction (ADC) calculations in the SF formalism where we use the ADC(2)-s, ADC(2)-x and ADC(3) schemes. A theoretical best estimate (TBE) is given for the AB and for each vertical energies.
|
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\end{abstract}
|
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|
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\maketitle
|
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@ -224,9 +224,9 @@ The cyclobutadiene (CBD) molecule represents a playground for ground state and e
|
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Despite the fact that excited states are involved in ubiquitious processes such as photochemistry, catalysis or in solar cell technology, none of the many methods existing is the reference in providing accurate excitation energies. Indeed, each method has its own flaws and there are so many chemical scenario that can occur, so it is still one of the biggest challenge in theoretical chemistry. Speaking of difficult task, cyclobutadiene (CBD) molecule has been a real challenge for experimental and theoretical chemists for many decades \cite{bally_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.
|
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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}.
|
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|
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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.
|
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At the ground state structrure ($D_{2h}$), the ${}^1A_g$ state has a weak multi-configurational character because of the well separated frontier orbitals and can be described by single-reference methods. But at the square ($D_{4h}$) geometry, the singlet state ${}^1B_{1g}$ has two singly occupied frontier orbitals that are degenerated so has a two-configurational character and single-reference methods are unreliable to describe it. The singlet ($D_{4h}$) is a transition state in the automerization reaction between the two rectangular structures (see Fig.\ref{fig:CBD}). The autoisomerization barrier (AB) for the CBD molecule is defined as the energy difference between the singlet ground state of the square ($D_{4h}$) structure and the singlet ground state of the rectangular ($D_{2h}$) geometry. The energy of this barrier was predicted, experimentally, in the range of 1.6-10 kcal.mol$^{-1}$ \cite{whitman_1982} and multi-reference calculations gave an energy barrier in the range of 6-7 kcal.mol$^{-1}$ \cite{eckert-maksic_2006}. All the specificities of the CBD molecule make it a real playground for excited-states methods.
|
||||
|
||||
Excited states of the CBD molecule in both geometries are represented in Fig.\ref{fig:CBD}. Are represented ${}^1A_g$ and $1{}^3B_{1g}$ states for the rectangular geometry and ${}^1B_{1g}$and $1{}^3A_{2g}$ for the square one. Due to energy scaling doubly excited 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}.
|
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Excited states of the CBD molecule in both geometries are represented in Fig.\ref{fig:CBD}. Are represented ${}^1A_g$ and $1{}^3B_{1g}$ states for the rectangular geometry and ${}^1B_{1g}$and $1{}^3A_{2g}$ for the square one. Due to energy scaling doubly excited state $1{}^1B_{1g}$ and $2{}^1A_{1g}$ for the $D_{2h}$ and $D_{4h}$ structures, respectively, are not drawn. Doubly excited states are known to be challenging to represent for adiabatic time-dependent density functional theory (TD-DFT) and even for state-of-the-art methods like the approximate third-order coupled-cluster (CC3) \cite{christiansen_1995,koch_1997} or equation-of-motion coupled-cluster with singles, doubles and triples (EOM-CCSDT) \cite{kucharski_1991,kallay_2004,hirata_2000,hirata_2004}.
|
||||
|
||||
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.
|
||||
|
||||
@ -234,9 +234,9 @@ Another way to deal with double excitations is to use high level truncation of t
|
||||
|
||||
An alternative to multiconfigurational and CC methods is the use of selected CI (SCI) methods for the computation of transition energies for singly and doubly excited states that are known to reach near full CI energies for small molecules. These methods allow to avoid an exponential increase of the size of the CI expansion by retaining the most energetically relevant determinants only, using a second-order energetic criterion to select perturbatively determinants in the FCI space.
|
||||
|
||||
Finally, to describe doubly excited states, one can think of spin-flip formalism established by Krylov in 2001. To briefly introduce the spin-flip idea we can present it like: instead of taking the singlet ground state as reference, the reference configuration is taken as the lowest triplet state. So one can access the singlet ground state and the singlet doubly-excited state via a spin-flip deexcitation and excitation (respectively), the difference of these two excitation energies providing an estimate of the double excitation. Obviously spin-flip methods have their own flaws, especially the spin contamination \cite{casanova_2020} (i.e., an artificial mixing of electronic states of differents spin multiplicities) due to spin incompleteness of the spin-flip expansion and by spin contamination of the reference configuration. One can adress part of this problem by expansion of the excitation order but with an increase of the computational cost or by complementing the spin-incomplete configuration set with the missing configurations.
|
||||
Finally, to describe doubly excited states, one can think of spin-flip formalism established by Krylov in 2001 \cite{casanova_2020}. To briefly introduce the spin-flip idea we can present it like: instead of taking the singlet ground state as reference, the reference configuration is taken as the lowest triplet state. So one can access the singlet ground state and the singlet doubly-excited state via a spin-flip deexcitation and excitation (respectively), the difference of these two excitation energies providing an estimate of the double excitation. Obviously spin-flip methods have their own flaws, especially the spin contamination \cite{casanova_2020} (i.e., an artificial mixing of electronic states of differents spin multiplicities) due to spin incompleteness of the spin-flip expansion and by spin contamination of the reference configuration. One can adress part of this problem by expansion of the excitation order but with an increase of the computational cost or by complementing the spin-incomplete configuration set with the missing configurations.
|
||||
|
||||
In the present work we investigate ${}^1A_g$, $1{}^3B_{1g}$, $1{}^1B_{1g}$, $2{}^1A_{g}$ and ${}^1B_{1g}$, $1{}^3A_{2g}$, $2{}^1A_{1g}$,$1{}^1B_{2g}$ excited states for the $D_{2h}$ and $D_{4h}$ geometries, respectively. Computational details are reported in Section \ref{sec:compmet} for SCI (Subsection \ref{sec:SCI}), EOM-CC (Subsection \ref{sec:CC}), multiconfigurational (Subsection \ref{sec:Multi}) and spin-flip (Subsection \ref{sec:sf}) methods. Section \ref{sec:res} is devoted to the discussion of our results, first we consider the ground state property studied which is the autoisomerization barrier (Subsection \ref{sec:auto}) and then we study the excited states (Subsection \ref{sec:states}) of the CBD molecule for both geometries.
|
||||
In the present work we investigate ${}^1A_g$, $1{}^3B_{1g}$, $1{}^1B_{1g}$, $2{}^1A_{g}$ and ${}^1B_{1g}$, $1{}^3A_{2g}$, $2{}^1A_{1g}$,$1{}^1B_{2g}$ excited states for the $D_{2h}$ and $D_{4h}$ geometries, respectively. Computational details are reported in Section \ref{sec:compmet} for SCI (Subsection \ref{sec:SCI}), EOM-CC (Subsection \ref{sec:CC}), multiconfigurational (Subsection \ref{sec:Multi}) and spin-flip (Subsection \ref{sec:sf}) methods. Section \ref{sec:res} is devoted to the discussion of our results, first we consider the ground state property studied which is the AB (Subsection \ref{sec:auto}) and then we study the excited states (Subsection \ref{sec:states}) of the CBD molecule for both geometries.
|
||||
|
||||
\begin{figure}
|
||||
\includegraphics[width=0.6\linewidth]{figure2.png}
|
||||
@ -253,7 +253,7 @@ In the present work we investigate ${}^1A_g$, $1{}^3B_{1g}$, $1{}^1B_{1g}$, $2{}
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsection{Selected Configuration Interaction}
|
||||
\label{sec:SCI}
|
||||
States energies and excitations energies calculations in the SCI framework are performed using QUANTUM PACKAGE where the CIPSI algorithm is implemented. The CIPSI algorithm allows to avoid the exponential increase of th CI expansion. To treat electronic states in the same way we use a state-averaged formalism meaning that the ground and excited states are represented with the same number and same set of determinants but using different CI coefficients. Then the SCI energy is the sum of two terms, the variational energy obtained by diagonalization of the CI matrix in the reference space and a second-order perturbative correction which estimates the contribution of the determinants not included in the CI space (estimate error in the truncation). It is possible to estimate the FCI limit for the total energies and compute the corresponding transition energies by extrapolating this second-order correction to zero. Extrapolation brings error and we can estime this one by energy difference between excitation energies obtained with the largest SCI wave function and the FCI extrapolated value. These errors provide a rough idea of the quality of the FCI extrapolation and cannot be seen as true bar error, they are reported in the following tables.
|
||||
States energies and excitations energies calculations in the SCI framework are performed using QUANTUM PACKAGE \cite{garniron_2019} where the CIPSI algorithm is implemented. The CIPSI algorithm allows to avoid the exponential increase of the CI expansion. To treat electronic states in the same way we use a state-averaged formalism meaning that the ground and excited states are represented with the same number and same set of determinants but using different CI coefficients. Then the SCI energy is the sum of two terms, the variational energy obtained by diagonalization of the CI matrix in the reference space and a second-order perturbative correction which estimates the contribution of the determinants not included in the CI space (estimate error in the truncation). It is possible to estimate the FCI limit for the total energies and compute the corresponding transition energies by extrapolating this second-order correction to zero. Extrapolation brings error and we can estime this one by energy difference between excitation energies obtained with the largest SCI wave function and the FCI extrapolated value. These errors provide a rough idea of the quality of the FCI extrapolation and cannot be seen as true bar error, they are reported in the following tables.
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
@ -272,13 +272,13 @@ State-averaged complete-active-space self-consistent field (SA-CASSCF) calculati
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsection{Spin-Flip}
|
||||
\label{sec:sf}
|
||||
In both structures the CBD has a singlet ground state, for the spin-flip calculations we consider the lowest triplet state as reference. Spin-flip techniques are broadly accessible and here, among them, we explore equation-of-motion coupled-cluster singles and doubles (EOM-CCSD), configuration interaction singles (CIS), algebraic-diagrammatic construction (ADC) scheme and TD-DFT. The standard and extended spin-flip ADC(2) (SF-ADC(2)-s and SF-ADC(2)-x respectively) and SF-ADC(3) are performed using Q-CHEM 5.2.1. Spin-flip TD-DFT calculations are also performed using Q-CHEM 5.2.1. The B3LYP, PBE0 and BH\&HLYP Hybrid GGA functionals are considered, they contain 20\%, 25\%, 50\% of exact exchange and are labeled, respectively, as SF-BLYP, SF-B3LYP, SF-PBE0, SF-BH\&HLYP. We also have done spin-flip TD-DFT calculations using Range-Separated Hybrid (RSH) functionals as: CAM-B3LYP, LC-$\omega$PBE08 and $\omega$B97X-V. The main difference here between these RSH functionals is the amount of exact-exchange at long-range: 75$\%$ for CAM-B3LYP and 100$\%$ for LC-$\omega$PBE08 and $\omega$B97X-V.
|
||||
%To complete the use of spin-flip TD-DFT we also considered the Hybrid meta-GGA functional M06-2X and the RSH meta-GGA functional M11. EOM-SF-CCSD and EOM-SF-CC(2,3) are also performed with Q-CHEM 5.2.1.
|
||||
In both structures the CBD has a singlet ground state, for the spin-flip calculations we consider the lowest triplet state as reference. Spin-flip techniques are broadly accessible and here, among them, we explore equation-of-motion coupled-cluster singles and doubles (EOM-CCSD), configuration interaction singles (CIS), algebraic-diagrammatic construction (ADC) scheme and TD-DFT. The standard and extended spin-flip ADC(2) (SF-ADC(2)-s and SF-ADC(2)-x respectively) and SF-ADC(3) are performed using Q-CHEM 5.2.1 \cite{shao_2015}. Spin-flip TD-DFT calculations are also performed using Q-CHEM 5.2.1. The B3LYP \cite{becke_1988b,lee_1988a,becke_1993b}, PBE0 \cite{adamo_1999a,ernzerhof_1999} and BH\&HLYP hybrid GGA functionals are considered, they contain 20\%, 25\%, 50\% of exact exchange and are labeled, respectively, as SF-BLYP, SF-B3LYP, SF-PBE0, SF-BH\&HLYP. We also have done spin-flip TD-DFT calculations using range-separated hybrid (RSH) functionals as: CAM-B3LYP \cite{yanai_2004a}, LC-$\omega$PBE08 and $\omega$B97X-V. The main difference here between these RSH functionals is the amount of exact-exchange at long-range: 75$\%$ for CAM-B3LYP and 100$\%$ for LC-$\omega$PBE08 and $\omega$B97X-V. To complete the use of spin-flip TD-DFT we also considered the hybrid meta-GGA functional M06-2X \cite{zhao_2008} and the RSH meta-GGA functional M11 \cite{peverati_2011}.
|
||||
%EOM-SF-CCSD and EOM-SF-CC(2,3) are also performed with Q-CHEM 5.2.1.
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsection{Theoretical Best Estimate (TBE)}
|
||||
All the calculations are performed using four basis set, the 6-31+G(d) basis and the aug-cc-pVXZ with X$=$D, T, Q. In the following we will use the notation AVXZ for the aug-cc-pVXZ basis, again with X$=$D, T, Q. For each studied quantity, i.e., the autoisomerisation barrier and the vertical excitations, we provide a theoretical best estimate (TBE). These TBEs are provided using extrapolated CCSDTQ/AVTZ values when possible and using NEVPT2(12,12) otherwise. The extrapolation of the CCSDTQ/AVTZ values is done using two schemes. The first one uses CC4 values for the extrapolation and proceed as follows
|
||||
All the calculations are performed using four basis set, the 6-31+G(d) basis and the aug-cc-pVXZ with X$=$D, T, Q \cite{dunning_1989}. In the following we will use the notation AVXZ for the aug-cc-pVXZ basis, again with X$=$D, T, Q. For each studied quantity, i.e., the autoisomerisation barrier and the vertical excitations, we provide a theoretical best estimate (TBE). These TBEs are provided using extrapolated CCSDTQ/AVTZ values when possible and using NEVPT2(12,12) otherwise. The extrapolation of the CCSDTQ/AVTZ values is done using two schemes. The first one uses CC4 values for the extrapolation and proceed as follows
|
||||
|
||||
\begin{equation}
|
||||
\label{eq:AVTZ}
|
||||
|
||||
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