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Abstract
We report a closed-form formula for the Zhang–Zhang polynomial (also known as ZZ polynomial or Clar covering polynomial) of an important class of elementary peri-condensed benzenoids Rbn1,n2,m1,m2, usually referred to as ribbons. A straightforward derivation is based on the recently developed interface theory of benzenoids [Langner and Witek, MATCH Commun. Math. Comput. Chem.2020, 84, 143–176]. The discovered formula provides compact expressions for various topological invariants of Rbn1,n2,m1,m2: the number of Kekulé structures, the number of Clar covers, its Clar number, and the number of Clar structures. The last two classes of elementary benzenoids, for which closed-form ZZ polynomial formulas remain to be found, are hexagonal flakes Ok,m,n and oblate rectangles Orm,n.
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2
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Kimber P, Plasser F. Toward an understanding of electronic excitation energies beyond the molecular orbital picture. Phys Chem Chem Phys 2020; 22:6058-6080. [DOI: 10.1039/d0cp00369g] [Citation(s) in RCA: 37] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023]
Abstract
Can we gain an intuitive understanding of excitation energies beyond the molecular picture?
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Affiliation(s)
- Patrick Kimber
- Department of Chemistry
- Loughborough University
- Loughborough
- UK
| | - Felix Plasser
- Department of Chemistry
- Loughborough University
- Loughborough
- UK
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3
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Nikolaienko TY. The maximum occupancy condition for the localized property-optimized orbitals. Phys Chem Chem Phys 2019; 21:5285-5294. [PMID: 30778429 DOI: 10.1039/c8cp07276k] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
Abstract
It is shown analytically that the Chemist's Localized Property-optimized Orbitals (CLPOs), which are the localized orbitals obtainable from the results of ab initio calculations by the open-source program JANPA (http://janpa.sourceforge.net/) according to the recently proposed optimal property partitioning condition, form the Lewis structure with nearly maximum possible total electron occupancy. The conditions required for this additional optimality to hold are discussed. In particular, when a single-determinant wavefunction is used to describe the molecular system without a noticeable electron delocalization, CLPOs derived from this wavefunction approximately optimize the same target quantity as the Natural Bond Orbitals (NBOs), establishing in this way the link between the two sets of localized orbitals. The performance of CLPO and NBO methods is compared by using a dataset containing 7101 small molecules, and the relevant methodological features of both methods are discussed.
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Affiliation(s)
- Tymofii Yu Nikolaienko
- Faculty of Physics of Taras Shevchenko National University of Kyiv, 64/13 Volodymyrska Str., Kyiv 01601, Ukraine.
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Poidevin C, Paciok P, Heggen M, Auer AA. High resolution transmission electron microscopy and electronic structure theory investigation of platinum nanoparticles on carbon black. J Chem Phys 2019; 150:041705. [DOI: 10.1063/1.5047666] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Corentin Poidevin
- Max-Planck-Institut für Kohlenforschung, 45470 Mülheim an der Ruhr, Germany
| | - Paul Paciok
- Ernst Ruska-Centre for Microscopy and Spectroscopy With Electrons and Peter Grünberg Institute, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
| | - Marc Heggen
- Ernst Ruska-Centre for Microscopy and Spectroscopy With Electrons and Peter Grünberg Institute, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
| | - Alexander A. Auer
- Max-Planck-Institut für Kohlenforschung, 45470 Mülheim an der Ruhr, Germany
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Pinheiro M, Cardoso DVV, Aquino AJA, Machado FBC, Lischka H. The characterization of electronic defect states of single and double carbon vacancies in graphene sheets using molecular density functional theory. Mol Phys 2019. [DOI: 10.1080/00268976.2019.1567848] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Max Pinheiro
- Departamento de Química, Instituto Tecnológico de Aeronáutica, São Paulo, Brazil
| | | | - Adélia J. A. Aquino
- Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, TX, USA
- School of Pharmaceutical Sciences and Technology, Tianjin University, Tianjin, People’s Republic of China
- Institute for Theoretical Chemistry, University of Vienna Vienna, Austria
| | | | - Hans Lischka
- Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, TX, USA
- School of Pharmaceutical Sciences and Technology, Tianjin University, Tianjin, People’s Republic of China
- Institute for Theoretical Chemistry, University of Vienna Vienna, Austria
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6
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Sandoval-Salinas ME, Carreras A, Casanova D. Triangular graphene nanofragments: open-shell character and doping. Phys Chem Chem Phys 2019; 21:9069-9076. [DOI: 10.1039/c9cp00641a] [Citation(s) in RCA: 29] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023]
Abstract
In this work we study the intricacies of the electronic structure properties of triangular graphene nanofragments (TGNFs) in their ground and low-lying excited states by means ofab initioquantum chemistry calculations.
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Affiliation(s)
- María E. Sandoval-Salinas
- Departament de Ciència de Materials i Química Física and Institut de Química Teòrica i Computacional (IQTCUB) Universitat de Barcelona
- Barcelona
- Spain
- Donostia International Physics Center (DIPC)
- Paseo Manuel de Lardizabal 4
| | - Abel Carreras
- Donostia International Physics Center (DIPC)
- Paseo Manuel de Lardizabal 4
- 20018 Donostia
- Spain
| | - David Casanova
- Donostia International Physics Center (DIPC)
- Paseo Manuel de Lardizabal 4
- 20018 Donostia
- Spain
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Lischka H, Nachtigallová D, Aquino AJA, Szalay PG, Plasser F, Machado FBC, Barbatti M. Multireference Approaches for Excited States of Molecules. Chem Rev 2018; 118:7293-7361. [DOI: 10.1021/acs.chemrev.8b00244] [Citation(s) in RCA: 197] [Impact Index Per Article: 32.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Affiliation(s)
- Hans Lischka
- School of Pharmaceutical Sciences and Technology, Tianjin University, Tianjin 300072, P.R. China
- Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409, United States
- Institute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Straße 17, 1090 Vienna, Austria
| | - Dana Nachtigallová
- Institute of Organic Chemistry and Biochemistry v.v.i., The Czech Academy of Sciences, Flemingovo nám. 2, 16610 Prague 6, Czech Republic
- Regional Centre of Advanced Technologies and Materials, Palacký University, 78371 Olomouc, Czech Republic
| | - Adélia J. A. Aquino
- School of Pharmaceutical Sciences and Technology, Tianjin University, Tianjin 300072, P.R. China
- Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409, United States
- Institute for Soil Research, University of Natural Resources and Life Sciences Vienna, Peter-Jordan-Strasse 82, A-1190 Vienna, Austria
| | - Péter G. Szalay
- ELTE Eötvös Loránd University, Laboratory of Theoretical Chemistry, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary
| | - Felix Plasser
- Institute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Straße 17, 1090 Vienna, Austria
- Department of Chemistry, Loughborough University, Leicestershire LE11 3TU, United Kingdom
| | - Francisco B. C. Machado
- Departamento de Química, Instituto Tecnológico de Aeronáutica, São José dos Campos 12228-900, São Paulo, Brazil
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8
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Abstract
The Hückel (tight-binding) molecular orbital (HMO) method has found many applications in the chemistry of alternant conjugated molecules, such as polycyclic aromatic hydrocarbons (PAHs), fullerenes and graphene-like molecules, as well as in solid-state physics. In this paper, we found analytical expressions for the electron density matrix of the HMO method in terms of odd-powers of its Hamiltonian. We prove that the HMO density matrix induces an embedding of a molecule into a high-dimensional Euclidean space in which the separation between the atoms scales very well with the bond lengths of PAHs. We extend our approach to describe a quasi-correlated tight-binding model, which quantifies the number of unpaired electrons and the distribution of effectively unpaired electrons. In this case, we found that the corresponding density matrices induce embedding of the molecules into high-dimensional Euclidean spheres where the separation between the atoms contains information about the spin–spin repulsion between them. Using our approach, we found an analytic expression which explains the bond length alternation in polyenes inside the HMO framework. We also found that spin–spin interaction explains the alternation of distances between pairs of atoms separated by two bonds in conjugated molecules.
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Plasser F, Mewes SA, Dreuw A, González L. Detailed Wave Function Analysis for Multireference Methods: Implementation in the Molcas Program Package and Applications to Tetracene. J Chem Theory Comput 2017; 13:5343-5353. [DOI: 10.1021/acs.jctc.7b00718] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Affiliation(s)
- Felix Plasser
- Institute
for Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währingerstrasse 17, 1090 Vienna, Austria
| | - Stefanie A. Mewes
- Interdisciplinary
Center for Scientific Computing, Ruprecht-Karls-University, Im Neuenheimer Feld 205 A, 69120 Heidelberg, Germany
- Centre
for Theoretical Chemistry and Physics, The New Zealand Institute for
Advanced Study (NZIAS), Massey University Albany, Private Bag 102904, Auckland 0745, New Zealand
| | - Andreas Dreuw
- Interdisciplinary
Center for Scientific Computing, Ruprecht-Karls-University, Im Neuenheimer Feld 205 A, 69120 Heidelberg, Germany
| | - Leticia González
- Institute
for Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währingerstrasse 17, 1090 Vienna, Austria
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