1
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Proos Vedin N, Escayola S, Radenković S, Solà M, Ottosson H. The n,π* States of Heteroaromatics: When are They the Lowest Excited States and in What Way Can They Be Aromatic or Antiaromatic? J Phys Chem A 2024. [PMID: 38787346 DOI: 10.1021/acs.jpca.4c02580] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/25/2024]
Abstract
Heteroaromatic molecules are found in areas ranging from biochemistry to photovoltaics. We analyze the n,π* excited states of 6π-electron heteroaromatics with in-plane lone pairs (nσ, herein n) and use qualitative theory and quantum chemical computations, starting at Mandado's 2n + 1 rule for aromaticity of separate spins. After excitation of an electron from n to π*, a (4n + 2)π-electron species has 2n + 2 πα-electrons and 2n + 1 πβ-electrons (or vice versa) and becomes πα-antiaromatic and πβ-aromatic. Yet, the antiaromatic πα- and aromatic πβ-components seldom cancel, leading to residuals with aromatic or antiaromatic character. We explore vertically excited triplet n,π* states (3n,π*), which are most readily analyzed, but also singlet n,π* states (1n,π*), and explain which compounds have n,π* states with aromatic residuals as their lowest excited states (e.g., pyrazine and the phenyl anion). If the πβ-electron population becomes more (less) uniformly distributed upon excitation, the system will have an (anti)aromatic residual. Among isomers, the one that has the most aromatic residual in 3n,π* is often of the lowest energy in this state. Five-membered ring heteroaromatics with one or two N, O, and/or S atoms never have n,π* states as their first excited states (T1 and S1), while this is nearly always the case for six-membered ring heteroaromatics with electropositive heteroatoms and/or highly symmetric (D2h) diheteroaromatics. For the complete compound set, there is a modest correlation between the (anti)aromatic character of the n,π* state and the energy gap between the lowest n,π* and π,π* states (R2 = 0.42), while it is stronger for monosubstituted pyrazines (R2 = 0.84).
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Affiliation(s)
- Nathalie Proos Vedin
- Department of Chemistry─Ångström Laboratory, Uppsala University, 751 20 Uppsala, Sweden
| | - Sílvia Escayola
- Institut de Quìmica Computacional i Catàlisi and Departament de Química, Universitat de Girona, C/Maria Aurèlia Capmany, 69, 17003 Girona, Catalonia, Spain
- Donostia International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain
| | - Slavko Radenković
- Faculty of Science, University of Kragujevac, P.O. Box 60, 34000 Kragujevac, Serbia
| | - Miquel Solà
- Institut de Quìmica Computacional i Catàlisi and Departament de Química, Universitat de Girona, C/Maria Aurèlia Capmany, 69, 17003 Girona, Catalonia, Spain
| | - Henrik Ottosson
- Department of Chemistry─Ångström Laboratory, Uppsala University, 751 20 Uppsala, Sweden
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2
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Kleinpeter E, Koch A. 1H and 13C NMR spectra of infinitene and the ring current effect of the aromatic molecule. MAGNETIC RESONANCE IN CHEMISTRY : MRC 2024. [PMID: 38782584 DOI: 10.1002/mrc.5467] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/11/2024] [Revised: 05/08/2024] [Accepted: 05/08/2024] [Indexed: 05/25/2024]
Abstract
The spatial magnetic properties (through-space NMR shieldings-TSNMRSs-actually the ring current effect in 1H NMR spectroscopy) of the recently synthesized infinitene (the helically twisted [12]circulene) have been calculated using the GIAO perturbation method employing the nucleus-independent chemical shift (NICS) concept and visualized as iso-chemical-shielding surfaces (ICSS) of various size and direction. Both 1H and 13C chemical shifts of infinitene and the aromaticity of this esthetically very appealing molecule have been studied subject to the ring current effect thus obtained. This spatial magnetic response property of TSNMRSs dominates the different magnitude of 1H and 13C chemical shifts, especially in the cross-over section of infinitene, which is unequivocally classified as an aromatic molecule based on the deshielding belt of its ring current effect. Differences in aromaticity of infinitene compared with isolated benzene can also be qualified and quantified on the magnetic criterion.
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Affiliation(s)
- Erich Kleinpeter
- Institut für Chemie, Universität Potsdam, Potsdam (Golm), Germany
| | - Andreas Koch
- Institut für Chemie, Universität Potsdam, Potsdam (Golm), Germany
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3
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Radenković S, Đorđević S, Nikolendžić M. Effect of Benzo-Annelation on Triplet State Energies in Polycyclic Conjugated Hydrocarbons. Chemistry 2024; 30:e202400361. [PMID: 38488676 DOI: 10.1002/chem.202400361] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2024] [Indexed: 04/09/2024]
Abstract
In a series of earlier studies, the effect of benzo-annelation was found to be a useful tool for tuning the aromaticity in polycyclic conjugated compounds to desired level. In this work we studied the (anti)aromaticity of benzo-annelated derivatives of three conjugated hydrocarbons (anthracene, fluoranthene and biphenylene) in their lowest lying singlet (S0) and triplet (T1) states by means of the energy effect (ef), harmonic oscillator model of aromaticity (HOMA), multicentre delocalization indices (MCI), magnetically induced current densities (MICDs) and nucleus independent chemical shifts (NICS). We showed that benzo-annelation is a topology-based effect which can be used to modify the T1 state excitation energies (E(T1)). A quantitative model was established being able to accurately predict the E(T1) based only on the numbers of angularly, linearly and geminally annelated benzene rings. In addition, it was demonstrated that the E(T1) can be directly related to the (anti)aromatic character of the central ring in the studied molecules in their S0 state.
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Affiliation(s)
- Slavko Radenković
- University of Kragujevac, Faculty of Science, P.O. Box 60, Kragujevac, 34000, Serbia
| | - Slađana Đorđević
- University of Kragujevac, Faculty of Science, P.O. Box 60, Kragujevac, 34000, Serbia
| | - Marijana Nikolendžić
- University of Kragujevac, Faculty of Science, P.O. Box 60, Kragujevac, 34000, Serbia
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4
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Wang Q, Sundholm D, Gauss J, Nottoli T, Lipparini F, Kino S, Ukai S, Fukui N, Shinokubo H. Changing aromatic properties through stacking: the face-to-face dimer of Ni(II) bis(pentafluorophenyl)norcorrole. Phys Chem Chem Phys 2024; 26:14777-14786. [PMID: 38716819 DOI: 10.1039/d4cp00968a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/23/2024]
Abstract
Nuclear magnetic resonance (NMR) shielding constants have been calculated for Ni(II) bis(pentafluorophenyl)norcorrole and its face-to-face stacked dimer at the Hartree-Fock (HF), second-order Møller-Plesset perturbation theory (MP2), complete-active-space self-consistent-field (CASSCF) levels as well as at density functional theory (DFT) levels using several functionals. The calculated 1H NMR shielding constants agree rather well with the experimental ones. The shielding constants of N and Ni calculated at DFT, HF, and MP2 levels differ from those obtained in the CASSCF calculations due to near-degeneracy effects at the Ni atom. The calculated magnetically induced current densities show that the monomer is antiaromatic, sustaining a strong global paratropic ring current, and the dimer is aromatic, sustaining a strong diatropic ring current. Qualitatively the same current density is obtained at the employed levels of theory. The most accurate ring-current strengths are probably obtained at the MP2 level. The aromatic dimer has a short intermolecular distance of less than 3 Å. The intermolecular interaction changes the nature of the frontier orbitals leading to a formal double bond between the norcorrole macrocycles.
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Affiliation(s)
- Qian Wang
- Department of Chemistry, Faculty of Science, University of Helsinki, P.O. Box 55 (A.I. Virtanens plats 1), FIN-00014, Finland.
| | - Dage Sundholm
- Department of Chemistry, Faculty of Science, University of Helsinki, P.O. Box 55 (A.I. Virtanens plats 1), FIN-00014, Finland.
| | - Jürgen Gauss
- Department Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, D-55128 Mainz, Germany
| | - Tommaso Nottoli
- Dipartimento di Chimica e Chimica Industriale, Università di Pisa, Via G. Moruzzi 13, I-56124 Pisa, Italy
| | - Filippo Lipparini
- Dipartimento di Chimica e Chimica Industriale, Università di Pisa, Via G. Moruzzi 13, I-56124 Pisa, Italy
| | - Shota Kino
- Department of Molecular and Macromolecular Chemistry, Graduate School of Engineering and Integrated Research Consortium on Chemical Sciences (IRCCS), Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8603, Japan
| | - Shusaku Ukai
- Department of Molecular and Macromolecular Chemistry, Graduate School of Engineering and Integrated Research Consortium on Chemical Sciences (IRCCS), Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8603, Japan
| | - Norihito Fukui
- Department of Molecular and Macromolecular Chemistry, Graduate School of Engineering and Integrated Research Consortium on Chemical Sciences (IRCCS), Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8603, Japan
- Graduate School of Engineering, Nagoya University, 2JST PRESTO, Japan
| | - Hiroshi Shinokubo
- Department of Molecular and Macromolecular Chemistry, Graduate School of Engineering and Integrated Research Consortium on Chemical Sciences (IRCCS), Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8603, Japan
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5
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Jana M, Blasco D, Sundholm D, Rath H. Organometallic copper(II) complex of meso- meso N-methyl N-confused pyrrole-bridged doubly N-methyl N-confused hexaphyrin. Org Biomol Chem 2024. [PMID: 38766981 DOI: 10.1039/d4ob00691g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/22/2024]
Abstract
Synthesis, spectroscopic and theoretical characterization of a hitherto unknown meso-meso N-confused N-methylpyrrole-bridged doubly N-confused hexaphyrin (molecule 5) and its organometallic copper(II) complex (molecule 6) are reported herein. The absence of Q-type bands in the UV-Vis spectrum and the high chemical shifts of the inner proton signals of 5 suggest its globally non-aromaticity. The spectroscopic evidence of non-aromaticity for 5 and the paramagnetic nature of 6, are fully supported by density functional theory (DFT) calculations of the UV-Vis spectra, electron paramagnetic resonance (EPR) g-tensor parameters, and the magnetically induced current density strengths obtained with the gauge-including magnetically induced currents (GIMIC) method.
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Affiliation(s)
- Manik Jana
- School of Chemical Sciences, Indian Association for the Cultivation of Science, 2A/2B Raja S.C Mullick Road, Jadavpur, Kolkata, West Bengal 700 032, India.
| | - Daniel Blasco
- Departamento de Química, Instituto de Investigación en Química (IQUR), Universidad de La Rioja, Madre de Dios 53, 26006, Logroño, Spain
| | - Dage Sundholm
- Department of Chemistry, Faculty of Science, University of Helsinki, P. O. Box 55 (A. I. Virtasen aukio 1), FIN-00014, Helsinki, Finland.
| | - Harapriya Rath
- School of Chemical Sciences, Indian Association for the Cultivation of Science, 2A/2B Raja S.C Mullick Road, Jadavpur, Kolkata, West Bengal 700 032, India.
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6
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Yadav R, Maiti A, Schorpp M, Graf J, Weigend F, Greb L. Supramolecular trapping of a cationic all-metal σ-aromatic {Bi 4} ring. Nat Chem 2024:10.1038/s41557-024-01530-z. [PMID: 38760432 DOI: 10.1038/s41557-024-01530-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/19/2023] [Accepted: 04/05/2024] [Indexed: 05/19/2024]
Abstract
Aromaticity in organic molecules is well defined, but its role in metal-only rings remains controversial. Here we introduce a supramolecular stabilization approach of a cationic {Bi4} rhomboid within the symmetric charge sphere of two bowl-shaped dianionic calix[4]pyrrolato indinates. Crystallographic and spectroscopic characterization, quantum chemical analysis and magnetically induced ring currents indicate σ-aromaticity in the formally tetracationic 16-valence electron [Bi4]4+ ring. Computational screening for other p-block elements identifies the planar rhomboid as the globally preferred structure for 16-valence electron four-atomic clusters. The aromatic [Bi4]4+ is isoelectronic to the [Al4]4-, a motif previously observed as antiaromatic in Li3[Al4]- in the gas phase. Thus, subtle factors such as charge isotropy seem to decide over aromaticity or antiaromaticity, advising for caution in debates based on the Hückel model-a concept valid for second-row elements but less deterministic for the heavier congeners.
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Affiliation(s)
- Ravi Yadav
- Anorganisch-Chemisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany
- School of Chemistry, Indian Institute of Science Education and Research Thiruvananthapuram, Thiruvananthapuram, India
| | - Avijit Maiti
- Anorganisch-Chemisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany
| | | | - Jürgen Graf
- Organisch-Chemisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany
| | - Florian Weigend
- Fachbereich Chemie, Philipps-Universität Marburg, Marburg, Germany.
| | - Lutz Greb
- Anorganisch-Chemisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany.
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7
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Kleinpeter E, Koch A. Identification and quantification of local antiaromaticity in polycyclic aromatic hydrocarbons (PAHs) based on the magnetic criterion. Org Biomol Chem 2024; 22:3035-3044. [PMID: 38534070 DOI: 10.1039/d4ob00114a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/28/2024]
Abstract
The spatial magnetic properties, through-space NMR shieldings (TSNMRSs, actually the ring current effect in 1H NMR spectroscopy), of a selection of entirely antiaromatic and aromatic polycyclic conjugated hydrocarbons (PCHs), and aromatic PCHs with antiaromatic components, have been calculated using the GIAO perturbation method employing the nucleus independent chemical shift (NICS) concept and visualized as iso-chemical-shielding surfaces (ICSSs) of various sizes and directions. Using both in-plane and above/below-plane ICSS data, polycyclic aromatic hydrocarbons can be readily distinguished from polycyclic antiaromatic ones, even when antiaromatic components are present in the polycyclic aromatic hydrocarbons (PAHs). These antiaromatic zones can also be attributed to internal components of the in-plane deshielding belt present in aromatic compounds and possible partial antiaromatic ring current effects in the same place. This makes it possible to unequivocally confirm correctly assigned or adjust incorrectly assigned antiaromaticity of individual rings in the same molecule.
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Affiliation(s)
- Erich Kleinpeter
- Universität Potsdam, Institut für Chemie, Karl-Liebknecht-Str. 24-25, D-14476 Potsdam (Golm), Germany.
| | - Andreas Koch
- Universität Potsdam, Institut für Chemie, Karl-Liebknecht-Str. 24-25, D-14476 Potsdam (Golm), Germany.
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8
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Kino S, Ukai S, Fukui N, Haruki R, Kumai R, Wang Q, Horike S, Phung QM, Sundholm D, Shinokubo H. Close Stacking of Antiaromatic Ni(II) Norcorrole Originating from a Four-Electron Multicentered Bonding Interaction. J Am Chem Soc 2024; 146:9311-9317. [PMID: 38502926 PMCID: PMC10996016 DOI: 10.1021/jacs.4c01142] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2024] [Revised: 03/04/2024] [Accepted: 03/05/2024] [Indexed: 03/21/2024]
Abstract
A π-conjugated molecule with one electronic spin often forms a π-stacked dimer through molecular orbital interactions between two unpaired electrons. The bonding is recognized as a multicentered two-electron interaction between the two π-conjugated molecules. Here, we disclose a multicentered bonding interaction between two antiaromatic molecules involving four electrons. We have synthesized an antiaromatic porphyrin analogue, Ni(II) bis(pentafluorophenyl)norcorrole. Its dimer adopts a face-to-face stacked structure with an extremely short stacking distance of 2.97 Å. The close stacking originates from a multicenter four-electron bonding interaction between the two molecules. The bonding electrons were experimentally observed via synchrotron X-ray diffraction analysis and corroborated by theoretical calculations. The intermolecular interaction of the molecular orbitals imparts the stacked dimer with aromatic character that is distinctly different from that of its monomer.
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Affiliation(s)
- Shota Kino
- Department
of Molecular and Macromolecular Chemistry, Graduate School of Engineering
and Integrated Research Consortium on Chemical Sciences (IRCCS), Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8603, Japan
| | - Shusaku Ukai
- Department
of Molecular and Macromolecular Chemistry, Graduate School of Engineering
and Integrated Research Consortium on Chemical Sciences (IRCCS), Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8603, Japan
| | - Norihito Fukui
- Department
of Molecular and Macromolecular Chemistry, Graduate School of Engineering
and Integrated Research Consortium on Chemical Sciences (IRCCS), Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8603, Japan
- PRESTO, Japan
Science and Technology Agency (JST), Kawaguchi, Saitama 332-0012, Japan
| | - Rie Haruki
- Photon
Factory, Institute of Materials Structure
Science, High Energy Accelerator Research Organization (KEK), Tsukuba, 305-0801, Japan
| | - Reiji Kumai
- Photon
Factory, Institute of Materials Structure
Science, High Energy Accelerator Research Organization (KEK), Tsukuba, 305-0801, Japan
| | - Qian Wang
- Department
of Chemistry, Faculty of Science, University
of Helsinki, Helsinki, FIN-00014, Finland
| | - Satoshi Horike
- Department
of Chemistry, Graduate School of Science, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto, 606-8502, Japan
| | - Quan Manh Phung
- Department
of Chemistry, Graduate School of Science, Nagoya University, Furo-cho,
Chikusa-ku, Nagoya, 464-8602, Japan
| | - Dage Sundholm
- Department
of Chemistry, Faculty of Science, University
of Helsinki, Helsinki, FIN-00014, Finland
| | - Hiroshi Shinokubo
- Department
of Molecular and Macromolecular Chemistry, Graduate School of Engineering
and Integrated Research Consortium on Chemical Sciences (IRCCS), Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8603, Japan
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9
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Miwa K, Yokota T, Wang Q, Sakurai T, Fliegl H, Sundholm D, Shinokubo H. Metallaantiaromaticity of 10-Platinacorrole Complexes. J Am Chem Soc 2024; 146:1396-1402. [PMID: 38172072 PMCID: PMC10882971 DOI: 10.1021/jacs.3c10250] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2024]
Abstract
The aromaticity of cyclic π-conjugated organometallic compounds is known as metallaaromaticity. π-Conjugated metallacycles, such as metallabenzenes and metallapentalenes, have been investigated in order to understand the involvement of the d electrons from the metal center in the π-conjugated systems of the organic ligands. Here, we report the synthesis of Pd(II) 10-platinacorrole complexes with cyclooctadiene (COD) and norbornadiene (NBD) ligands. While the Pd(II) 10-platinacorrole COD complex adopts a distorted structure without showing appreciable antiaromaticity, the corresponding NBD complex exhibits a distinct antiaromatic character due to its highly planar conformation. Detailed density functional theory (DFT) calculations revealed that two d orbitals are involved in macrocyclic π-conjugation. We furthermore demonstrated that Craig-Möbius antiaromaticity is not present in the studied system. The synthesis of 10-platinacorroles enables a systematic comparison of the antiaromaticity and aromaticity of closely related porphyrin analogues, providing a better understanding of π-conjugation that involves d orbitals.
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Affiliation(s)
- Kazuki Miwa
- Department of Molecular and Macromolecular Chemistry, Graduate School of Engineering and Integrated Research Consortium on Chemical Sciences (IRCCS), Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8603 Aichi, Japan
| | - Tomoya Yokota
- Department of Molecular and Macromolecular Chemistry, Graduate School of Engineering and Integrated Research Consortium on Chemical Sciences (IRCCS), Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8603 Aichi, Japan
| | - Qian Wang
- Department of Chemistry, Faculty of Science, University of Helsinki, FIN-00014 Helsinki, Finland
| | - Takahiro Sakurai
- Department of Molecular and Macromolecular Chemistry, Graduate School of Engineering and Integrated Research Consortium on Chemical Sciences (IRCCS), Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8603 Aichi, Japan
| | - Heike Fliegl
- FIZ Karlsruhe─Leibniz Institute for Information Infrastructure, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany
| | - Dage Sundholm
- Department of Chemistry, Faculty of Science, University of Helsinki, FIN-00014 Helsinki, Finland
| | - Hiroshi Shinokubo
- Department of Molecular and Macromolecular Chemistry, Graduate School of Engineering and Integrated Research Consortium on Chemical Sciences (IRCCS), Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8603 Aichi, Japan
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10
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Huynh BC, Wibowo-Teale M, Wibowo-Teale AM. QSym 2: A Quantum Symbolic Symmetry Analysis Program for Electronic Structure. J Chem Theory Comput 2024; 20:114-133. [PMID: 38145888 PMCID: PMC10782455 DOI: 10.1021/acs.jctc.3c01118] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2023] [Revised: 11/16/2023] [Accepted: 11/29/2023] [Indexed: 12/27/2023]
Abstract
Symmetry provides a powerful machinery to classify, interpret, and understand quantum-mechanical theories and results. However, most contemporary quantum chemistry packages lack the ability to handle degeneracy and symmetry breaking effects, especially in non-Abelian groups, and they are not able to characterize symmetry in the presence of external magnetic or electric fields. In this article, a program written in Rust entitled QSym2 that makes use of group and representation theories to provide symmetry analysis for a wide range of quantum-chemical calculations is introduced. With its ability to generate character tables symbolically on-the-fly and by making use of a generic symmetry-orbit-based representation analysis method formulated in this work, QSym2 is able to address all of these shortcomings. To illustrate these capabilities of QSym2, four sets of case studies are examined in detail in this article: (i) high-symmetry C84H64, C60, and B9- to demonstrate the analysis of degenerate molecular orbitals (MOs); (ii) octahedral Fe(CN)63- to demonstrate the analysis of symmetry-broken determinants and MOs; (iii) linear hydrogen fluoride in a magnetic field to demonstrate the analysis of magnetic symmetry; and (iv) equilateral H3+ to demonstrate the analysis of density symmetries.
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Affiliation(s)
- Bang C. Huynh
- School
of Chemistry, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Meilani Wibowo-Teale
- School
of Chemistry, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Andrew M. Wibowo-Teale
- School
of Chemistry, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
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11
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Schattenberg C, Wodyński A, Åström H, Sundholm D, Kaupp M, Lehtola S. Revisiting Gauge-Independent Kinetic Energy Densities in Meta-GGAs and Local Hybrid Calculations of Magnetizabilities. J Phys Chem A 2023; 127:10896-10907. [PMID: 38100678 PMCID: PMC10758120 DOI: 10.1021/acs.jpca.3c06244] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2023] [Revised: 10/27/2023] [Accepted: 11/08/2023] [Indexed: 12/17/2023]
Abstract
In a recent study [J. Chem. Theory Comput. 2021, 17, 1457-1468], some of us examined the accuracy of magnetizabilities calculated with density functionals representing the local density approximation (LDA), generalized gradient approximation (GGA), meta-GGA (mGGA), as well as global hybrid (GH) and range-separated (RS) hybrid functionals by assessment against accurate reference values obtained with coupled-cluster theory with singles, doubles, and perturbative triples [CCSD(T)]. Our study was later extended to local hybrid (LH) functionals by Holzer et al. [J. Chem. Theory Comput. 2021, 17, 2928-2947]; in this work, we examine a larger selection of LH functionals, also including range-separated LH (RSLH) functionals and strong-correlation LH (scLH) functionals. Holzer et al. also studied the importance of the physically correct handling of the magnetic gauge dependence of the kinetic energy density (τ) in mGGA calculations by comparing the Maximoff-Scuseria formulation of τ used in our aforementioned study to the more physical current-density extension derived by Dobson. In this work, we also revisit this comparison with a larger selection of mGGA functionals. We find that the newly tested LH, RSLH, and scLH functionals outperform all of the functionals considered in the previous studies. The various LH functionals afford the seven lowest mean absolute errors while also showing remarkably small standard deviations and mean errors. Most strikingly, the best two functionals are scLHs that also perform remarkably well in cases with significant multiconfigurational character, such as the ozone molecule, which is traditionally excluded from statistical error evaluations due to its large errors with common density functionals.
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Affiliation(s)
- Caspar
J. Schattenberg
- Institut
für Chemie, Theoretische Chemie/Quantenchemie, Technische Universität Berlin, Sekr. C7, Straße des 17. Juni 135, D-10623 Berlin, Germany
| | - Artur Wodyński
- Institut
für Chemie, Theoretische Chemie/Quantenchemie, Technische Universität Berlin, Sekr. C7, Straße des 17. Juni 135, D-10623 Berlin, Germany
| | - Hugo Åström
- Department
of Chemistry, Faculty of Science, University
of Helsinki, P.O. Box 55
(A.I. Virtanens plats 1), University of Helsinki FI-00014, Finland
| | - Dage Sundholm
- Department
of Chemistry, Faculty of Science, University
of Helsinki, P.O. Box 55
(A.I. Virtanens plats 1), University of Helsinki FI-00014, Finland
| | - Martin Kaupp
- Institut
für Chemie, Theoretische Chemie/Quantenchemie, Technische Universität Berlin, Sekr. C7, Straße des 17. Juni 135, D-10623 Berlin, Germany
| | - Susi Lehtola
- Department
of Chemistry, Faculty of Science, University
of Helsinki, P.O. Box 55
(A.I. Virtanens plats 1), University of Helsinki FI-00014, Finland
- Molecular
Sciences Software Institute, Blacksburg, Virginia 24061, United States
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12
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Franzke YJ, Holzer C. Exact two-component theory becoming an efficient tool for NMR shieldings and shifts with spin-orbit coupling. J Chem Phys 2023; 159:184102. [PMID: 37937936 DOI: 10.1063/5.0171509] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2023] [Accepted: 09/04/2023] [Indexed: 11/09/2023] Open
Abstract
We present a gauge-origin invariant exact two-component (X2C) approach within a modern density functional framework, supporting meta-generalized gradient approximations such as TPSS and range-separated hybrid functionals such as CAM-B3LYP. The complete exchange-correlation kernel is applied, including the direct contribution of the field-dependent basis functions and the reorthonormalization contribution from the perturbed overlap matrix. Additionally, the finite nucleus model is available for the electron-nucleus potential and the vector potential throughout. Efficiency is ensured by the diagonal local approximation to the unitary decoupling transformation in X2C as well as the (multipole-accelerated) resolution of the identity approximation for the Coulomb term (MARI-J, RI-J) and the seminumerical exchange approximation. Errors introduced by these approximations are assessed and found to be clearly negligible. The applicability of our implementation to large-scale calculations is demonstrated for a tin pincer-type system as well as low-valent tin and lead complexes. Here, the calculation of the Sn nuclear magnetic resonance shifts for the pincer-type ligand with about 2400 basis functions requires less than 1 h for hybrid density functionals. Further, the impact of spin-orbit coupling on the nucleus-independent chemical shifts and the corresponding ring currents of all-metal aromatic systems is studied.
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Affiliation(s)
- Yannick J Franzke
- Fachbereich Chemie, Philipps-Universität Marburg, Hans-Meerwein-Straße 4, 35032 Marburg, Germany
| | - Christof Holzer
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology (KIT), Wolfgang-Gaede-Straße 1, 76131 Karlsruhe, Germany
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13
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Franzke Y, Holzer C, Andersen JH, Begušić T, Bruder F, Coriani S, Della Sala F, Fabiano E, Fedotov DA, Fürst S, Gillhuber S, Grotjahn R, Kaupp M, Kehry M, Krstić M, Mack F, Majumdar S, Nguyen BD, Parker SM, Pauly F, Pausch A, Perlt E, Phun GS, Rajabi A, Rappoport D, Samal B, Schrader T, Sharma M, Tapavicza E, Treß RS, Voora V, Wodyński A, Yu JM, Zerulla B, Furche F, Hättig C, Sierka M, Tew DP, Weigend F. TURBOMOLE: Today and Tomorrow. J Chem Theory Comput 2023; 19:6859-6890. [PMID: 37382508 PMCID: PMC10601488 DOI: 10.1021/acs.jctc.3c00347] [Citation(s) in RCA: 23] [Impact Index Per Article: 23.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2023] [Indexed: 06/30/2023]
Abstract
TURBOMOLE is a highly optimized software suite for large-scale quantum-chemical and materials science simulations of molecules, clusters, extended systems, and periodic solids. TURBOMOLE uses Gaussian basis sets and has been designed with robust and fast quantum-chemical applications in mind, ranging from homogeneous and heterogeneous catalysis to inorganic and organic chemistry and various types of spectroscopy, light-matter interactions, and biochemistry. This Perspective briefly surveys TURBOMOLE's functionality and highlights recent developments that have taken place between 2020 and 2023, comprising new electronic structure methods for molecules and solids, previously unavailable molecular properties, embedding, and molecular dynamics approaches. Select features under development are reviewed to illustrate the continuous growth of the program suite, including nuclear electronic orbital methods, Hartree-Fock-based adiabatic connection models, simplified time-dependent density functional theory, relativistic effects and magnetic properties, and multiscale modeling of optical properties.
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Affiliation(s)
- Yannick
J. Franzke
- Fachbereich
Chemie, Philipps-Universität Marburg, Hans-Meerwein-Str. 4, 35032 Marburg, Germany
| | - Christof Holzer
- Institute
of Theoretical Solid State Physics, Karlsruhe
Institute of Technology (KIT), Wolfgang-Gaede-Str. 1, 76131 Karlsruhe, Germany
| | - Josefine H. Andersen
- DTU
Chemistry, Department of Chemistry, Technical
University of Denmark, Kemitorvet Building 207, DK-2800 Kongens Lyngby, Denmark
| | - Tomislav Begušić
- Division
of Chemistry and Chemical Engineering, California
Institute of Technology, Pasadena, California 91125, United States
| | - Florian Bruder
- Fachbereich
Chemie, Philipps-Universität Marburg, Hans-Meerwein-Str. 4, 35032 Marburg, Germany
| | - Sonia Coriani
- DTU
Chemistry, Department of Chemistry, Technical
University of Denmark, Kemitorvet Building 207, DK-2800 Kongens Lyngby, Denmark
| | - Fabio Della Sala
- Institute
for Microelectronics and Microsystems (CNR-IMM), Via Monteroni, Campus Unisalento, 73100 Lecce, Italy
- Center for
Biomolecular Nanotechnologies @UNILE, Istituto
Italiano di Tecnologia, Via Barsanti, 73010 Arnesano, Italy
| | - Eduardo Fabiano
- Institute
for Microelectronics and Microsystems (CNR-IMM), Via Monteroni, Campus Unisalento, 73100 Lecce, Italy
- Center for
Biomolecular Nanotechnologies @UNILE, Istituto
Italiano di Tecnologia, Via Barsanti, 73010 Arnesano, Italy
| | - Daniil A. Fedotov
- DTU
Chemistry, Department of Chemistry, Technical
University of Denmark, Kemitorvet Building 207, DK-2800 Kongens Lyngby, Denmark
- Institute
of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Susanne Fürst
- Institut
für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Technische Universität Berlin, Straße des 17 Juni 135, 10623, Berlin, Germany
| | - Sebastian Gillhuber
- Institute
of Inorganic Chemistry, Karlsruhe Institute
of Technology (KIT), Engesserstr. 15, 76131 Karlsruhe, Germany
| | - Robin Grotjahn
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Martin Kaupp
- Institut
für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Technische Universität Berlin, Straße des 17 Juni 135, 10623, Berlin, Germany
| | - Max Kehry
- Institute
of Physical Chemistry, Karlsruhe Institute
of Technology (KIT), Fritz-Haber-Weg 2, 76131 Karlsruhe, Germany
| | - Marjan Krstić
- Institute
of Theoretical Solid State Physics, Karlsruhe
Institute of Technology (KIT), Wolfgang-Gaede-Str. 1, 76131 Karlsruhe, Germany
| | - Fabian Mack
- Institute
of Physical Chemistry, Karlsruhe Institute
of Technology (KIT), Fritz-Haber-Weg 2, 76131 Karlsruhe, Germany
| | - Sourav Majumdar
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Brian D. Nguyen
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Shane M. Parker
- Department
of Chemistry, Case Western Reserve University, 10900 Euclid Ave, Cleveland, Ohio 44106 United States
| | - Fabian Pauly
- Institute
of Physics, University of Augsburg, Universitätsstr. 1, 86159 Augsburg, Germany
| | - Ansgar Pausch
- Institute
of Physical Chemistry, Karlsruhe Institute
of Technology (KIT), Fritz-Haber-Weg 2, 76131 Karlsruhe, Germany
| | - Eva Perlt
- Otto-Schott-Institut
für Materialforschung, Friedrich-Schiller-Universität
Jena, Löbdergraben
32, 07743 Jena, Germany
| | - Gabriel S. Phun
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Ahmadreza Rajabi
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Dmitrij Rappoport
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Bibek Samal
- Department
of Chemical Sciences, Tata Institute of
Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
| | - Tim Schrader
- Otto-Schott-Institut
für Materialforschung, Friedrich-Schiller-Universität
Jena, Löbdergraben
32, 07743 Jena, Germany
| | - Manas Sharma
- Otto-Schott-Institut
für Materialforschung, Friedrich-Schiller-Universität
Jena, Löbdergraben
32, 07743 Jena, Germany
| | - Enrico Tapavicza
- Department
of Chemistry and Biochemistry, California
State University, Long Beach, 1250 Bellflower Boulevard, Long
Beach, California 90840-9507, United States
| | - Robert S. Treß
- Lehrstuhl
für Theoretische Chemie, Ruhr-Universität
Bochum, 44801 Bochum, Germany
| | - Vamsee Voora
- Department
of Chemical Sciences, Tata Institute of
Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
| | - Artur Wodyński
- Institut
für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Technische Universität Berlin, Straße des 17 Juni 135, 10623, Berlin, Germany
| | - Jason M. Yu
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Benedikt Zerulla
- Institute
of Nanotechnology, Karlsruhe Institute of
Technology (KIT), Hermann-von-Helmholtz-Platz
1, 76344 Eggenstein-Leopoldshafen Germany
| | - Filipp Furche
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Christof Hättig
- Lehrstuhl
für Theoretische Chemie, Ruhr-Universität
Bochum, 44801 Bochum, Germany
| | - Marek Sierka
- Otto-Schott-Institut
für Materialforschung, Friedrich-Schiller-Universität
Jena, Löbdergraben
32, 07743 Jena, Germany
| | - David P. Tew
- Physical
and Theoretical Chemistry Laboratory, University
of Oxford, South Parks
Road, Oxford OX1 3QZ, United Kingdom
| | - Florian Weigend
- Fachbereich
Chemie, Philipps-Universität Marburg, Hans-Meerwein-Str. 4, 35032 Marburg, Germany
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14
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Sudhakaran KP, Benny A, John AT, Hariharan M. Exploring the influence of graphene on antiaromaticity of pentalene. Phys Chem Chem Phys 2023; 25:26986-26990. [PMID: 37812393 DOI: 10.1039/d3cp02760k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/10/2023]
Abstract
Theoretical investigations on the influence of graphene fragments on the antiaromaticity of pentalene are conducted by employing multiple aromaticity descriptors based on magnetic, geometric and electronic criteria. NICS as a sole descriptor for analysing the antiaromaticity of pentalene on graphene fragments has to be carefully considered while looking through the other aromaticity indicators.
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Affiliation(s)
- Keerthy P Sudhakaran
- School of Chemistry, Indian Institute of Science Education and Research Thiruvananthapuram, Vithura, Thiruvananthapuram, Kerala, 695551, India.
| | - Alfy Benny
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
| | - Athira T John
- School of Chemistry, Indian Institute of Science Education and Research Thiruvananthapuram, Vithura, Thiruvananthapuram, Kerala, 695551, India.
| | - Mahesh Hariharan
- School of Chemistry, Indian Institute of Science Education and Research Thiruvananthapuram, Vithura, Thiruvananthapuram, Kerala, 695551, India.
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15
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Mahmood A, Dimitrova M, Sundholm D. Current-Density Calculations on Zn-Porphyrin 40 Nanorings. J Phys Chem A 2023; 127:7452-7459. [PMID: 37665662 PMCID: PMC10510378 DOI: 10.1021/acs.jpca.3c03564] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2023] [Revised: 08/04/2023] [Indexed: 09/06/2023]
Abstract
Two porphyrinoid nanorings have been studied computationally. They were built by linking 40 Zn-porphyrin units with butadiyne bridges. The molecular structures belonging to the D40h point group were fully optimized with the Turbomole program at the density functional theory (DFT) level using the B3LYP functional and the def2-SVP basis sets. The aromatic character was studied at the DFT level by calculating the magnetically induced current-density (MICD) susceptibility using the GIMIC program. The neutral molecules are globally non-aromatic with aromatic Zn-porphyrin units. Charged nanorings could not be studied because almost degenerate frontier orbitals led to vanishing optical gaps for the cations. Since DFT calculations of the MICD are computationally expensive, we also calculated the MICD using three pseudo-π models. Appropriate pseudo-π models were constructed by removing the outer hydrogen atoms and replacing all carbon and nitrogen atoms with hydrogen atoms. The central Zn atom was either replaced with a beryllium atom or with two inner hydrogen atoms. Calculations with the computationally inexpensive pseudo-π models yielded qualitatively the same magnetic response as obtained in the all-electron calculations.
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Affiliation(s)
- Atif Mahmood
- Department of Chemistry, University
of Helsinki, P.O. Box 55, A. I. Virtasen Aukio 1, FIN-00014 Helsinki, Finland
| | - Maria Dimitrova
- Department of Chemistry, University
of Helsinki, P.O. Box 55, A. I. Virtasen Aukio 1, FIN-00014 Helsinki, Finland
| | - Dage Sundholm
- Department of Chemistry, University
of Helsinki, P.O. Box 55, A. I. Virtasen Aukio 1, FIN-00014 Helsinki, Finland
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16
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Grotjahn R, Furche F. Gauge-Invariant Excited-State Linear and Quadratic Response Properties within the Meta-Generalized Gradient Approximation. J Chem Theory Comput 2023. [PMID: 37399786 DOI: 10.1021/acs.jctc.3c00259] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/05/2023]
Abstract
Gauge invariance is a fundamental symmetry connected to charge conservation and is widely accepted as indispensable for any electronic structure method. Hence, the gauge variance of the time-dependent kinetic energy density τ used in many meta-generalized gradient approximations (MGGAs) to the exchange-correlation (XC) functional presents a major obstacle for applying MGGAs within time-dependent density functional theory (TDDFT). Replacing τ by the gauge-invariant generalized kinetic energy density τ̂ significantly improves the accuracy of various functionals for vertical excitation energies [R. Grotjahn, F. Furche, and M. Kaupp. J. Chem. Phys. 2022, 157, 111102]. However, the dependence of the resulting current-MGGAs (cMGGAs) on the paramagnetic current density gives rise to new exchange-correlation kernels and hyper-kernels ignored in previous implementations of quadratic and higher-order response properties. Here we report the first implementation of cMGGAs and hybrid cMGGAs for excited-state gradients and dipole moments, as well as an extension to quadratic response properties including dynamic hyperpolarizabilities and two-photon absorption cross sections. In the first comprehensive benchmark study of MGGAs and cMGGAs for two-photon absorption cross sections, the M06-2X functional is found to be superior to the GGA hybrid PBE0. Additionally, two case studies from the literature for the practical prediction of nonlinear optical properties are revisited and potential advantages of hybrid (c)MGGAs compared to hybrid GGAs are discussed. The effect of restoring gauge invariance varies depending on the employed MGGA functional, the type of excitation, and the property under investigation: While some individual excited-state equilibrium structures are significantly affected, on average, these changes result in marginal improvements when compared against high-level reference data. Although the gauge-variant MGGA quadratic response properties are generally close to their gauge-invariant counterparts, the resulting errors are not bounded and significantly exceed typical method errors in some of the cases studied. Despite the limited effects seen in benchmark studies, gauge-invariant implementations of cMGGAs for excited-state properties are desirable from a fundamental perspective, entail little additional computational cost, and are necessary for response properties consistent with cMGGA linear response calculations such as excitation energies.
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Affiliation(s)
- Robin Grotjahn
- Department of Chemistry, University of California, Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Filipp Furche
- Department of Chemistry, University of California, Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
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17
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Orozco-Ic M, Sundholm D. On the antiaromatic-aromatic-antiaromatic transition of the stacked cyclobutadiene dimer. Phys Chem Chem Phys 2023; 25:12777-12782. [PMID: 37128984 DOI: 10.1039/d3cp01350b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
We have studied the changes in the aromatic nature of two cyclobutadiene (C4H4) molecules on decreasing the intermolecular distance and approaching the cubane structure in a face-to-face fashion. The analysis based on the calculations of the magnetically induced current density and the induced magnetic field shows that the aromaticity of the two C4H4 rings changes from a strongly antiaromatic character at long distances to an aromatic transition state of stacked C4H4 rings at intermediate internuclear distances when approaching the antiaromatic state of cubane.
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Affiliation(s)
- Mesías Orozco-Ic
- Department of Chemistry, Faculty of Science, University of Helsinki, P.O. Box 55, A. I. Virtasen aukio 1, FIN-00014 Helsinki, Finland.
- Donostia International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain
| | - Dage Sundholm
- Department of Chemistry, Faculty of Science, University of Helsinki, P.O. Box 55, A. I. Virtasen aukio 1, FIN-00014 Helsinki, Finland.
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18
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Summa FF. Spin Currents Induced in Open-Shell Molecules by Static and Uniform Magnetic and Electric Fields in the Presence of a Spin-Orbit Coupling Interaction and Conservation Law. J Chem Theory Comput 2023; 19:2491-2501. [PMID: 37104848 PMCID: PMC10173463 DOI: 10.1021/acs.jctc.3c00017] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/29/2023]
Abstract
The derivation of the total induced current density vector field, in the presence of static and uniform magnetic and electric fields, is illustrated in a more clear and formally correct language together with a discussion on the charge-current conservation law not presented before for the spin-orbit coupling contribution. The theory here exposed turns out to be in fully agreement with the theory of Special Relativity and it is applicable to open-shell molecules in the presence of a nonvanishing spin orbit coupling. The discussion here exposed turns out to be accurately valid for a strictly central field due to the chosen approximation of the spin-orbit coupling Hamiltonian, but it is appropriate to deal correctly with molecular systems. The ab initio calculation of spin current densities has been implemented at both unrestricted Hartree-Fock and unrestricted DFT levels of theory. Some maps of spin currents on molecules of interest, i.e., the CH3 radical and the superoctazethrene molecule are also illustrated.
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Affiliation(s)
- Francesco Ferdinando Summa
- Dipartimento di Chimica e Biologia "A. Zambelli", Università degli Studi di Salerno, via Giovanni Paolo II 132, Fisciano 84084, SA Italy
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19
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Wang Q, Pyykkö J, Dimitrova M, Taubert S, Sundholm D. Current-density pathways in figure-eight-shaped octaphyrins. Phys Chem Chem Phys 2023; 25:12469-12478. [PMID: 37097103 DOI: 10.1039/d3cp01062g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/26/2023]
Abstract
We have calculated the current density induced by an external magnetic field in a set of figure-eight-shaped expanded porphyrinoids. The studied octaphyrins can be divided into three classes (N2, N4, and N6) based on the number of the inner hydrogen atoms of the pyrrole rings. Using the Runge-Kutta method, the current density is split into diatropic and paratropic contributions that are analyzed separately. The calculations show that one common ring current consists of two rather independent pathways. Each of them follows the outer side of the molecular frame of one half of the molecule and passes to the inner side of the frame on the other half. The ring-current pathways are similar to the ones for [12]infinitene. However, the current density of the octaphyrins is more complex having many branching points and pathways. Vertical through-space current-density pathways pass in the middle of the molecules through a plane that is parallel to the figure-eight-shaped view of the molecules when the magnetic field is perpendicular to the plane. The isolectronic N2 and the N4 dication sustain a weak paratropic ring current inside the molecule, which is also observed in the 1H NMR magnetic shielding constant of the inner hydrogen atoms. The diatropic current-density contribution dominates in the studied molecules. For the N4 and N6 molecules, the global current-density pathways are only diatropic and N6 sustains the strongest global diatropic current-density flux of 13.2 nA T-1.
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Affiliation(s)
- Qian Wang
- Department of Chemistry, Faculty of Science, P.O. Box 55 (A.I. Virtanens plats 1), FIN-00014 University of Helsinki, Finland.
| | - Jaakko Pyykkö
- Department of Chemistry, Faculty of Science, P.O. Box 55 (A.I. Virtanens plats 1), FIN-00014 University of Helsinki, Finland.
| | - Maria Dimitrova
- Department of Chemistry, Faculty of Science, P.O. Box 55 (A.I. Virtanens plats 1), FIN-00014 University of Helsinki, Finland.
| | - Stefan Taubert
- Department of Chemistry, Faculty of Science, P.O. Box 55 (A.I. Virtanens plats 1), FIN-00014 University of Helsinki, Finland.
| | - Dage Sundholm
- Department of Chemistry, Faculty of Science, P.O. Box 55 (A.I. Virtanens plats 1), FIN-00014 University of Helsinki, Finland.
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20
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Radenković S, Đorđević S. Effect of benzo-annelation on magnetically induced current density. Chem Phys Lett 2023. [DOI: 10.1016/j.cplett.2023.140370] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/17/2023]
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21
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Olejniczak M, Tierny J. Topological data analysis of vortices in the magnetically-induced current density in LiH molecule. Phys Chem Chem Phys 2023; 25:5942-5947. [PMID: 36722896 DOI: 10.1039/d2cp05893f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
Abstract
A novel strategy for extracting axial (AV) and toroidal (TV) vortices in the magnetically-induced current density (MICD) in molecular systems is introduced, and its pilot application to LiH molecule is demonstrated. It exploits differences in the topologies of AV and TV cores and involves two key steps: selecting a scalar function that can describe vortex cores in MICD and its subsequent topological analysis. The scalar function of choice is ΩBα based on the velocity-gradient Ω method known in research on classical flows. The Topological Data Analysis (TDA) is then used to analyze the ΩBα scalar field. In particular, TDA robustly assigns distinct topological features of this field to different vortex types in LiH: AV to saddle-maximum separatrices which connect maxima to 2-saddles located on the domain's boundary, TV to a 1-cycle of the super-level sets of the input data. Both are extracted as the most persistent features of the topologically-simplified ΩBα scalar field.
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Affiliation(s)
- Małgorzata Olejniczak
- Centre of New Technologies, University of Warsaw, S. Banacha 2c, Warsaw 02-097, Poland.
| | - Julien Tierny
- CNRS, Sorbonne Université, Laboratoire d'Informatique de Paris 6, LIP6, Paris F-75005, France
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22
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Kelly JA, Streitferdt V, Dimitrova M, Westermair FF, Gschwind RM, Berger RJF, Wolf R. Transition-Metal-Stabilized Heavy Tetraphospholide Anions. J Am Chem Soc 2022; 144:20434-20441. [DOI: 10.1021/jacs.2c08754] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- John A. Kelly
- Institute of Inorganic Chemistry, University of Regensburg, 93040 Regensburg, Germany
| | - Verena Streitferdt
- Institute of Organic Chemistry, University of Regensburg, 93040 Regensburg, Germany
| | - Maria Dimitrova
- Department of Chemistry, Faculty of Science, University of Helsinki, FI-00014 University of Helsinki, Finland
| | - Franz F. Westermair
- Institute of Organic Chemistry, University of Regensburg, 93040 Regensburg, Germany
| | - Ruth M. Gschwind
- Institute of Organic Chemistry, University of Regensburg, 93040 Regensburg, Germany
| | - Raphael J. F. Berger
- Department for Chemistry and Physics of Materials, Paris-Lodron University Salzburg, 5020 Salzburg, Austria
| | - Robert Wolf
- Institute of Inorganic Chemistry, University of Regensburg, 93040 Regensburg, Germany
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23
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Mahmood A, Dimitrova M, Wirz LN, Sundholm D. Magnetically Induced Current Densities in π-Conjugated Porphyrin Nanoballs. J Phys Chem A 2022; 126:7864-7873. [PMID: 36270016 PMCID: PMC9639160 DOI: 10.1021/acs.jpca.2c04856] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2022] [Revised: 10/05/2022] [Indexed: 11/29/2022]
Abstract
Magnetically induced current densities (MICDs) of Zn-porphyrinoid nanostructures have been studied at the density functional theory level using the B3LYP functional and the def2-SVP basis set. Six of the studied Zn-porphyrinoid nanostructures consist of two crossing porphyrinoid belts, and one is a porphyrinoid nanoball belonging to the octahedral (O) point group. The Zn-porphyrin units are connected to each other via butadiyne linkers as in a recently synthesized porphyrinoid structure resembling two crossed belts. The MICDs are calculated using the gauge-including magnetically induced current method. Current-density pathways and their strengths were determined by numerically integrating the MICD passing through selected planes that cross chemical bonds or molecular rings. The current-density calculations show that the studied neutral molecules are globally nonaromatic but locally aromatic sustaining ring currents only in the individual porphyrin rings or around two neighboring porphyrins. The ring-current strengths of the individual porphyrin rings are 20% weaker than in Zn-porphyrin, whereas oxidation leads to globally aromatic cations sustaining ring currents that are somewhat stronger than for Zn-porphyrin.
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Affiliation(s)
- Atif Mahmood
- Department of Chemistry, University
of Helsinki, A. I. Virtasen
Aukio 1, P.O. Box
55, FIN-00014 Helsinki, Finland
| | - Maria Dimitrova
- Department of Chemistry, University
of Helsinki, A. I. Virtasen
Aukio 1, P.O. Box
55, FIN-00014 Helsinki, Finland
| | - Lukas N. Wirz
- Department of Chemistry, University
of Helsinki, A. I. Virtasen
Aukio 1, P.O. Box
55, FIN-00014 Helsinki, Finland
| | - Dage Sundholm
- Department of Chemistry, University
of Helsinki, A. I. Virtasen
Aukio 1, P.O. Box
55, FIN-00014 Helsinki, Finland
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24
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Bai LX, Orozco-Ic M, Zarate X, Sundholm D, Pan S, Guo JC, Merino G. B 3Al 4+: A Three-Dimensional Molecular Reuleaux Triangle. Molecules 2022; 27:7407. [PMID: 36364234 PMCID: PMC9656129 DOI: 10.3390/molecules27217407] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2022] [Revised: 10/19/2022] [Accepted: 10/23/2022] [Indexed: 12/02/2023] Open
Abstract
We systematically explore the potential energy surface of the B3Al4+ combination of atoms. The putative global minimum corresponds to a structure formed by an Al4 square facing a B3 triangle. Interestingly, the dynamical behavior can be described as a Reuleaux molecular triangle since it involves the rotation of the B3 triangle at the top of the Al4 square. The molecular dynamics simulations, corroborating with the very small rotational barriers of the B3 triangle, show its nearly free rotation on the Al4 ring, confirming the fluxional character of the cluster. Moreover, while the chemical bonding analysis suggests that the multicenter interaction between the two fragments determines its fluxionality, the magnetic response analysis reveals this cluster as a true and fully three-dimensional aromatic system.
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Affiliation(s)
- Li-Xia Bai
- Nanocluster Laboratory, Institute of Molecular Science, Shanxi University, Taiyuan 030006, China
| | - Mesías Orozco-Ic
- Department of Chemistry, University of Helsinki, A. I. Virtasen Aukio 1, P.O. Box 55, FIN-00014 Helsinki, Finland
| | - Ximena Zarate
- Instituto de Ciencias Químicas Aplicadas, Facultad de Ingeniería, Universidad Autónoma de Chile, Av. Pedro de Valdivia 425, Santiago 7500912, Chile
| | - Dage Sundholm
- Department of Chemistry, University of Helsinki, A. I. Virtasen Aukio 1, P.O. Box 55, FIN-00014 Helsinki, Finland
| | - Sudip Pan
- Fachbereich Chemie, Philipps-Universitt Marburg Hans-Meerwein-Straße, 35043 Marburg, Germany
| | - Jin-Chang Guo
- Nanocluster Laboratory, Institute of Molecular Science, Shanxi University, Taiyuan 030006, China
| | - Gabriel Merino
- Departamento de Física Aplicada, Centro de Investigación y de Estudios Avanzados, Unidad Mérida. Km 6 Antigua Carretera a Progreso. Apdo., Postal 73, Cordemex, Merida 97310, Mexico
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25
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Orozco-Ic M, Sundholm D. Magnetic response properties of carbon nano-onions. Phys Chem Chem Phys 2022; 24:22487-22496. [PMID: 36106772 DOI: 10.1039/d2cp02718f] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The magnetic response of a number of double- and triple-layer carbon nano-onions (CNOs) is analyzed by calculating the magnetically induced current density and the induced magnetic field using the pseudo-π model. Qualitatively the same magnetic response was obtained in calculations at the all-electron level. The calculations show that the CNOs exhibit strong net diatropic (paratropic) ring currents when the external magnetic field points perpendicularly to one of the six-membered (five-membered) rings. They are deshielded inside and shielded outside the CNO; the latter dominates for larger CNOs. The magnetic response originates from a combination of spherical paratropic current densities on the inside of each carbon layer and diatropic current densities on the outside of them. The quantitative differences in the aromaticity of the CNOs as compared to single fullerenes are discussed in terms of ring-current strengths. The magnetic response of some of the CNOs is approximately the sum of the magnetic response of the individual layers, whereas deviations are significant for CNOs containing C80. For the largest CNOs, the deviation from the sum of the fullerene contributions is larger, especially when the external magnetic field is perpendicular to a six-membered ring.
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Affiliation(s)
- Mesías Orozco-Ic
- Department of Chemistry, Faculty of Science, University of Helsinki, P.O. Box 55, A. I. Virtasen aukio 1, FIN-00014 Helsinki, Finland.
| | - Dage Sundholm
- Department of Chemistry, Faculty of Science, University of Helsinki, P.O. Box 55, A. I. Virtasen aukio 1, FIN-00014 Helsinki, Finland.
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26
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Berger RJF, Dimitrova M. A natural scheme for the quantitative analysis of the magnetically induced molecular current density using an oriented flux-weighted stagnation graph. I. A minimal example for LiH. Phys Chem Chem Phys 2022; 24:23089-23095. [PMID: 36129405 DOI: 10.1039/d2cp02262a] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A new natural scheme is introduced to analyze quantitatively the magnetically induced molecular current density vector field, J. The set of zero points of J, which is called its stagnation graph (SG), has been previously used to study the topological features of the current density of various molecules. Here, the line integrals of the induced magnetic field along edges of the connected subset of the SG are calculated. The edges are oriented such that all weights, i.e., flux values become non-negative, thereby, an oriented flux-weighted (current density) stagnation graph (OFW-SG) is obtained. Since in the exact theoretical limit, J is divergence-free and due to the topological characteristics of such vector fields, the flux of all separate vortices (current density domains) and neighbouring connected vortices can be determined exactly by adding the weights of cyclic subsets of edges (i.e., closed loops) of the OFW-SG. The procedure is exemplified by the minimal example of LiH for a weak homogeneous external magnetic field, B, perpendicular to the chemical bond. The OFW-SG exhibits one closed loop (formally decomposed into two edges), and an open line extending to infinity on both of its ends. The method provides the means of accurately determining the strength of the current density even in molecules with a complicated set of distinct vortices.
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Affiliation(s)
- Raphael J F Berger
- Fachbereich für Chemie und Physik der Materialien, Paris-Lodron Universität Salzburg, Jakob-Harringerstr. 2a, A-5020 Salzburg, Österreich, Austria.
| | - Maria Dimitrova
- Department of Chemistry, Faculty of Science, University of Helsinki, P.O. Box 55, A. I. Virtasen aukio 1, FI-00014, Finland
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27
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Grotjahn R, Furche F, Kaupp M. Importance of imposing gauge invariance in time-dependent density functional theory calculations with meta-generalized gradient approximations. J Chem Phys 2022; 157:111102. [PMID: 36137777 DOI: 10.1063/5.0113083] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
It has been known for more than a decade that the gauge variance of the kinetic energy density τ leads to additional terms in the magnetic orbital rotation Hessian used in linear-response time-dependent density functional theory (TDDFT), affecting excitation energies obtained with τ-dependent exchange-correlation functionals. While previous investigations found that a correction scheme based on the paramagnetic current density has a small effect on benchmark results, we report more pronounced effects here, in particular, for the popular M06-2X functional and for some other meta-generalized gradient approximations (mGGAs). In the first part of this communication, this is shown by a reassessment of a set of five Ni(II) complexes for which a previous benchmark study that did not impose gauge invariance has found surprisingly large errors for excitation energies obtained with M06-2X. These errors are more than halved by restoring gauge invariance. The variable importance of imposing gauge invariance for different mGGA-based functionals can be rationalized by the derivative of the mGGA exchange energy integrand with respect to τ. In the second part, a large set of valence excitations in small main-group molecules is analyzed. For M06-2X, several selected n → π* and π→π⊥ * excitations are heavily gauge-dependent with average changes of -0.17 and -0.28 eV, respectively, while π→π‖ * excitations are marginally affected (-0.04 eV). Similar patterns, but of the opposite signs, are found for SCAN0. The results suggest that reevaluation of previous gauge variant TDDFT results based on M06-2X and other mGGA functionals is warranted.
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Affiliation(s)
- Robin Grotjahn
- Technische Universität Berlin, Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Straße des 17. Juni 135, 10623 Berlin, Germany
| | - Filipp Furche
- Department of Chemistry, University of California, Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, USA
| | - Martin Kaupp
- Technische Universität Berlin, Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Straße des 17. Juni 135, 10623 Berlin, Germany
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28
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Wypych K, Dimitrova M, Sundholm D, Pawlicki M. Diagnosing Ring Current(s) in Figure-Eight Skeletons: A 3D Through-Space Conjugation in the Two-Loops Crossing. Org Lett 2022; 24:4876-4880. [PMID: 35796415 PMCID: PMC9348834 DOI: 10.1021/acs.orglett.2c01625] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
![]()
The macrocyclic structures
with local conjugation readily undergo
a redox-triggered change in the diatropic character, leading to a
global current–density pathway of the doubly charged systems.
The figure-eight geometry of the neutral dimer does not significantly
change upon oxidation according to the spectroscopic and computational
data. The oxidation leads to 3D cross-conjugation at the intersection
of the two ethylene bridges resulting in a global ring current.
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Affiliation(s)
- Katarzyna Wypych
- Faculty of Chemistry, Jagiellonian University, Gronostajowa 2, 30-387 Kraków, Poland.,Department of Chemistry, University of Wrocław, F. Joliot-Curie 14, 503833 Wrocław, Poland
| | - Maria Dimitrova
- Department of Chemistry, University of Helsinki, P.O. Box 55, A. I. Virtasen aukio 1, FIN-00014 Helsinki, Finland
| | - Dage Sundholm
- Department of Chemistry, University of Helsinki, P.O. Box 55, A. I. Virtasen aukio 1, FIN-00014 Helsinki, Finland
| | - Miłosz Pawlicki
- Faculty of Chemistry, Jagiellonian University, Gronostajowa 2, 30-387 Kraków, Poland
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29
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Franzke YJ, Holzer C. Communication: Impact of the current density on paramagnetic NMR properties. J Chem Phys 2022; 157:031102. [DOI: 10.1063/5.0103898] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Meta-generalized gradient approximations (meta-GGAs) and local hybrid functionals generally depend on the kinetic energy density τ. For magnetic properties, this necessitates generalizations to ensure gauge invariance. In most implementations, τ is generalized by incorporating the external magnetic field. However, this introduces artifacts in the response of the density matrix and does not satisfy the iso-orbital constraint. Here, we extend previous approaches based on the current density to paramagnetic NMR shieldings and EPR g-tensors. The impact is assessed for main-group compounds and transition-metal complexes considering 25 density functional approximations. It is shown that the current density leads to substantial improvements-especially for the popular Minnesota and SCAN functional families. Thus, we strongly recommend to use the current density generalized τ in paramagnetic NMR and EPR calculations with meta-GGAs.
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Affiliation(s)
- Yannick J. Franzke
- Fachbereich Chemie, Philipps-Universität Marburg Fachbereich Chemie, Germany
| | - Christof Holzer
- Institute of Theoretical Solid State Physics, Karlsruher Institut für Technologie Fakultät für Physik, Germany
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30
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Đorđević S, Solà M, Radenković S. Aromaticity of Singlet and Triplet Boron Disk-like Clusters: A Test for Electron Counting Aromaticity Rules. Inorg Chem 2022; 61:10116-10125. [PMID: 35737864 DOI: 10.1021/acs.inorgchem.2c01197] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Boron clusters are polyhedral boron-containing structures that have unique features and properties. The disk-like boron clusters are among the most fascinating boron cluster forms. These clusters have a molecular orbital (MO) distribution similar to the one derived from the simple particle-on-a-disk model. In this model, the MOs come in pairs except for m = 0. Disk-like boron clusters in their singlet ground state are aromatic when they reach a closed-shell structure. One could expect that disk-like aromatic boron clusters in the singlet state, when acquiring or releasing two electrons, may also be aromatic in the lowest-lying triplet state. We use magnetically induced current densities and bond current strengths to analyze the aromatic character of a series of disk-like boron clusters. Our results show that, with the exception of triplet 3B19-, the disk-like boron clusters follow Hückel and Baird's rules if one considers the different MOs grouped by their symmetry. We also found that if the lowest-lying triplet state in disk-like boron clusters is aromatic, this triplet state is the ground state for this species.
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Affiliation(s)
- Slađana Đorđević
- Faculty of Science, University of Kragujevac, P.O. Box 60, Kragujevac 34000, Serbia
| | - Miquel Solà
- Institute of Computational Chemistry and Catalysis and Department of Chemistry, University of Girona, C/M. Aurèlia Capmany, 69, Girona 17003, Catalonia, Spain
| | - Slavko Radenković
- Faculty of Science, University of Kragujevac, P.O. Box 60, Kragujevac 34000, Serbia
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31
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Radenković S, Tomović Ž. Tuning the structure and properties of N-doped positively charged polycyclic aromatic hydrocarbons. Chemphyschem 2022; 23:e202200125. [PMID: 35404503 DOI: 10.1002/cphc.202200125] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2022] [Revised: 04/07/2022] [Indexed: 11/11/2022]
Abstract
A detailed study of the geometry, aromatic character, electronic and magnetic properties for a series of positively charged N-doped PAHs was performed. Magnetic properties of the examined molecules were analyzed by means of the magnetically induced current density calculated using the diamagnetic-zero version of the continuous transformation of origin of current density (CTOCD-DZ) method. The comparative study of the local aromaticity of the studied molecules was performed using several different indices: energy effect (ef), harmonic oscillator model of aromaticity (HOMA) index, six centre delocalization index (SCI) and nucleus independent chemical shifts (NICS). The presence of N-atoms in the inner rings was found to cause a planarity distortion in the studied N-doped systems. The geometric changes and charged nature of the studied N-doped systems do not significantly influence the current density and the local aromaticity distribution in comparison with the corresponding parent benzenoid hydrocarbons. The present study demonstrates how quantum chemical calculations can be used for rational design of novel PAHs and fine tuning of their properties.
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Affiliation(s)
- Slavko Radenković
- University of Kragujevac: Univerzitet u Kragujevcu, Department of Chemistry, 12 Radoja Domanovića, P.O. Box 60, 34000, Kragujevac, SERBIA
| | - Željko Tomović
- Eindhoven University of Technology: Technische Universiteit Eindhoven, Department of Chemical Engineering & Chemistry and Institute for Complex Molecular Systems, NETHERLANDS
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32
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Yang Y, Helili S, Kerim A. A study of the aromaticity of thia[7]circulene isomers. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2060146] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Yang Yang
- College of Chemistry, Xinjiang University, Urumqi, People’s Republic of China
| | - Satewaerdi Helili
- School of Chemical Engineering and Technology, Xinjiang University, Urumqi, People’s Republic of China
| | - Ablikim Kerim
- School of Chemical Engineering and Technology, Xinjiang University, Urumqi, People’s Republic of China
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33
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Mahmood A, Dimitrova M, Wirz LN, Sundholm D. Magnetically Induced Current Densities in Zinc Porphyrin Nanoshells. J Phys Chem A 2022; 126:1936-1945. [PMID: 35302768 PMCID: PMC8978182 DOI: 10.1021/acs.jpca.1c10815] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
![]()
The molecular structures
of porphyrinoid cages were obtained by
constructing small polyhedral graphs whose vertices have degree-4.
The initial structures were then fully optimized at the density functional
theory (DFT) level using the generalized gradient approximation. Some
of polyhedral vertices were replaced with Zn–porphyrin units
and their edges were replaced with ethyne or butadiyne bridges or
connected by fusing two neighboring Zn–porphyrin units. Molecule 1 is an ethyne-bridge porphyrinoid nanotube, whose ends are
sealed with a Zn–porphyrin. Molecule 2 is the
corresponding open porphyrinoid nanotube. Molecule 3 is
a clam-like porphyrinoid cage, whose shells consist of fused Zn–porphyrins,
and the two halves are connected via butadiyne bridges. Molecule 4 is a cross-belt of fused Zn–porphyrins, and molecule 5 is a cross-belt of Zn–porphyrins connected with butadiyne
bridges. The magnetically induced current density of the optimized
porphyrinoid cages was calculated for determining the aromatic character,
the degree of aromaticity and the current-density pathways. The current-density
calculations were performed at the DFT level with the gauge—including
magnetically induced currents (GIMIC) method using the B3LYP hybrid
functional and def2-SVP basis sets. Calculations of the current densities
show that molecule 2 sustains a paratropic ring current
around the nanotube, whereas sealing the ends as in molecule 1 leads to an almost nonaromatic nanotube. Fusing porphyrinoids
as in molecules 3 and 4 results in complicated
current-density pathways that differ from the ones usually appearing
in porphyrinoids. The aromatic character of molecules 4 and 5 changes upon oxidation. The neutral molecule 4 is antiaromatic, whereas the dication is nonaromatic. Molecule 5 is nonaromatic, and its dication is aromatic.
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Affiliation(s)
- Atif Mahmood
- Department of Chemistry, University of Helsinki, P.O. Box 55, A. I. Virtasen aukio 1, FIN-00014 Helsinki, Finland
| | - Maria Dimitrova
- Department of Chemistry, University of Helsinki, P.O. Box 55, A. I. Virtasen aukio 1, FIN-00014 Helsinki, Finland
| | - Lukas N Wirz
- Department of Chemistry, University of Helsinki, P.O. Box 55, A. I. Virtasen aukio 1, FIN-00014 Helsinki, Finland
| | - Dage Sundholm
- Department of Chemistry, University of Helsinki, P.O. Box 55, A. I. Virtasen aukio 1, FIN-00014 Helsinki, Finland
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34
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Orozco-Ic M, Valiev RR, Sundholm D. Non-intersecting ring currents in [12]infinitene. Phys Chem Chem Phys 2022; 24:6404-6409. [PMID: 35262148 DOI: 10.1039/d2cp00637e] [Citation(s) in RCA: 15] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023]
Abstract
The aromaticity of the newly synthesized [12]infinitene is addressed via analysis of the magnetically induced current density and the induced magnetic field. Our calculations reveal that [12]infinitene responds to an external magnetic field by creating two current-density pathways that flow diatropically along the edges of the molecule. The current-density pathways do not intersect. The entire structure is completely shielded suggesting that the infinitene molecule is aromatic, contrary to what the Möbius rule for twisted annulene structures predicts. We also studied the dication of [12]infinitene, which sustains two paratropic ring currents flowing along the edges. The space between the stacked rings at the crossing point is shorter for the dication as compared to the neutral molecule. Hence, a strong through-space current density appears at the crossing point of π-π stacked rings.
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Affiliation(s)
- Mesías Orozco-Ic
- Department of Chemistry, Faculty of Science, University of Helsinki, P.O. Box 55, A. I. Virtasen aukio 1, FIN-00014 Helsinki, Finland.
| | - Rashid R Valiev
- Department of Chemistry, Faculty of Science, University of Helsinki, P.O. Box 55, A. I. Virtasen aukio 1, FIN-00014 Helsinki, Finland. .,Research School of Chemistry and Applied Biomedical Sciences, National Research Tomsk Polytechnic University, Tomsk 634050, Russia
| | - Dage Sundholm
- Department of Chemistry, Faculty of Science, University of Helsinki, P.O. Box 55, A. I. Virtasen aukio 1, FIN-00014 Helsinki, Finland.
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35
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Radenković S, Đorđević S. Spatial and electronic structures of BeB8 and MgB8. How far the analogy goes? Chemphyschem 2022; 23:e202200070. [PMID: 35188320 DOI: 10.1002/cphc.202200070] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2022] [Revised: 02/18/2022] [Indexed: 11/09/2022]
Abstract
Doping of boron clusters with Be and its heavier alkaline-earth congener, Mg usually leads to complexes of different geometry and electronic structure. In this work we showed that both neutral BeB 8 and MgB 8 exhibit a singlet ground state umbrella-like form. In addition, the stability, electronic structure, and aromaticity of the target molecules were compared. The magnetically induced current densities showed that BeB 8 and MgB 8 are double aromatic systems: π and σ electrons induce strong diatropic currents. The current densities induced in the studied complexes are of very similar intensity, but with a different spatial distribution. The found differences between the current density patterns in BeB 8 and MgB 8 arise from the very nature of the bonding interactions between the M atom and B 8 fragment, as demonstrated through the energy decomposition analysis (EDA).
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Affiliation(s)
- Slavko Radenković
- University of Kragujevac: Univerzitet u Kragujevcu, Department of Chemistry, 12 Radoja Domanovića, P.O. Box 60, 34000, Kragujevac, SERBIA
| | - Slađana Đorđević
- University of Kragujevac: Univerzitet u Kragujevcu, Department of Chemistry, SERBIA
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