1
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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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2
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Hilla P, Vaara J. NMR chemical shift of confined 129Xe: coordination number, paramagnetic channels and molecular dynamics in a cryptophane-A biosensor. Phys Chem Chem Phys 2023; 25:22719-22733. [PMID: 37606522 DOI: 10.1039/d3cp02695g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/23/2023]
Abstract
Advances in hyperpolarisation and indirect detection have enabled the development of xenon nuclear magnetic resonance (NMR) biosensors (XBSs) for molecule-selective sensing in down to picomolar concentration. Cryptophanes (Crs) are popular cages for hosting the Xe "spy". Understanding the microscopic host-guest chemistry has remained a challenge in the XBS field. While early NMR computations of XBSs did not consider the important effects of host dynamics and explicit solvent, here we model the motionally averaged, relativistic NMR chemical shift (CS) of free Xe, Xe in a prototypic CrA cage and Xe in a water-soluble CrA derivative, each in an explicit H2O solvent, over system configurations generated at three different levels of molecular dynamics (MD) simulations. We confirm the "contact-type" character of the Xe CS, arising from the increased availability of paramagnetic channels, magnetic couplings between occupied and virtual orbitals through the short-ranged orbital hyperfine operator, when neighbouring atoms are in contact with Xe. Remarkably, the Xe CS in the present, highly dynamic and conformationally flexible situations is found to depend linearly on the coordination number of the Xe atom. We interpret the high- and low-CS situations in terms of the magnetic absorption spectrum and choose our preference among the used MD methods based on comparison with the experimental CS. We check the role of spin-orbit coupling by comparing with fully relativistic CS calculations. The study outlines the computational workflow required to realistically model the CS of Xe confined in dynamic cavity structures under experimental conditions, and contributes to microscopic understanding of XBSs.
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Affiliation(s)
- Perttu Hilla
- NMR Research Unit, P.O. Box 3000, FI-90014 University of Oulu, Finland.
| | - Juha Vaara
- NMR Research Unit, P.O. Box 3000, FI-90014 University of Oulu, Finland.
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3
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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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4
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Jena S, Routray C, Dutta J, Biswal HS. Hydrogen Bonding Directed Reversal of
13
C NMR Chemical Shielding. Angew Chem Int Ed Engl 2022; 61:e202207521. [DOI: 10.1002/anie.202207521] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2022] [Indexed: 12/30/2022]
Affiliation(s)
- Subhrakant Jena
- School of Chemical Sciences, National Institute of Science Education and Research (NISER) PO-Bhimpur-Padanpur Via-Jatni, District-Khurda PIN - 752050 Bhubaneswar India
- Homi Bhabha National Institute, Training School Complex Anushakti Nagar Mumbai 400094 India
| | - Chinmay Routray
- School of Chemical Sciences, National Institute of Science Education and Research (NISER) PO-Bhimpur-Padanpur Via-Jatni, District-Khurda PIN - 752050 Bhubaneswar India
- Homi Bhabha National Institute, Training School Complex Anushakti Nagar Mumbai 400094 India
| | - Juhi Dutta
- School of Chemical Sciences, National Institute of Science Education and Research (NISER) PO-Bhimpur-Padanpur Via-Jatni, District-Khurda PIN - 752050 Bhubaneswar India
- Homi Bhabha National Institute, Training School Complex Anushakti Nagar Mumbai 400094 India
| | - Himansu S. Biswal
- School of Chemical Sciences, National Institute of Science Education and Research (NISER) PO-Bhimpur-Padanpur Via-Jatni, District-Khurda PIN - 752050 Bhubaneswar India
- Homi Bhabha National Institute, Training School Complex Anushakti Nagar Mumbai 400094 India
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5
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Jena S, Routray C, Dutta J, Biswal HS. Hydrogen‐Bonding Directed Reversal of 13C NMR Chemical Shielding. Angew Chem Int Ed Engl 2022. [DOI: 10.1002/ange.202207521] [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)
- Subhrakant Jena
- National Institute of Science Education and Research School of Chemical Sciences INDIA
| | - Chinmay Routray
- National Institute of Science Education and Research School of Chemical Sciences INDIA
| | - Juhi Dutta
- National Institute of Science Education and Research School of Chemical Sciences INDIA
| | - Himansu Sekhar Biswal
- National Institute of Science Education and Research School of Chemical Sciences Jatani 752050 Bhubaneswar INDIA
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6
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Abstract
![]()
The origin-independent
current density induced by a perpendicular
magnetic field in the infinitene molecule has been calculated, confirming
the recently presented result by Orozco-Ic et al. (2022, 24, 6404−640935262148) of two disjointed global current pathways
along the edges formed by 24 carbon atoms having the form of the infinity
symbol. The current strength has been assessed along the C–C
bonds forming the two separate circuits, whose particular shape provides
a diamagnetic exaltation which is only 73% of the expected value for
this aromatic molecule. Through space currents have been
found along the bond paths determined by the electron density gradient,
whose strength is 10% that of the aromatic benzene ring current. It
is shown that the pair of high-field 1H NMR experimental
signals carry the signature of the two global currents, which are
counterrotating inside the fjord regions with respect to the rim of
the coronene subunits.
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Affiliation(s)
- Guglielmo Monaco
- Department of Chemistry and Biology "A. Zambelli", Università degli Studi di Salerno, via Giovanni Paolo II 132, Fisciano 84084, Salerno, Italy
| | - Riccardo Zanasi
- Department of Chemistry and Biology "A. Zambelli", Università degli Studi di Salerno, via Giovanni Paolo II 132, Fisciano 84084, Salerno, Italy
| | - Francesco F Summa
- Department of Chemistry and Biology "A. Zambelli", Università degli Studi di Salerno, via Giovanni Paolo II 132, Fisciano 84084, Salerno, Italy
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7
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Báez-Grez R, Pino-Rios R. The hidden aromaticity in borazine. RSC Adv 2022; 12:7906-7910. [PMID: 35424723 PMCID: PMC8982269 DOI: 10.1039/d1ra06457f] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2021] [Accepted: 02/25/2022] [Indexed: 02/05/2023] Open
Abstract
The aromaticity of borazine (B3N3H6), also known as the inorganic benzene, is a controversial issue since this compound has several characteristics that could qualify it as an aromatic compound. However, recent studies using magnetic criteria indicate that this compound should be considered as a non-aromatic system. This assignment is mainly due to diatropic currents in the nitrogen atoms without observation of ring currents. The present work shows by means of the magnetic criteria that borazine has a ring current hidden by the local contributions of degenerate orbitals π1 and π2. Additionally, the study of borazine's first triplet state antiaromaticity using the magnetic and energetic criteria by means of isomerization stabilization energies (ISEs) together with Baird's and Hückel's rules suggests that borazine is best described as an (weakly) aromatic system. Dissected magnetically induced current density calculations show that local currents in borazine counteract the ring current and therefore hide its (weak) aromatic character.![]()
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Affiliation(s)
- Rodrigo Báez-Grez
- Computational and Theoretical Chemistry Group, Departamento de Ciencias Químicas, Facultad de Ciencias Exactas, Universidad Andres Bello República 498 Santiago Chile
| | - Ricardo Pino-Rios
- Laboratorio de Química Teórica, Facultad de Química y Biología, Universidad de Santiago de Chile (USACH) Av. Libertador Bernardo O'Higgins 3363 Santiago Estación Central, Región Metropolitana Chile
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8
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Kleinpeter E, Koch A. Cyclazines‐Structure and Aromaticity or Antiaromaticity on the Magnetic Criterion. European J Org Chem 2022. [DOI: 10.1002/ejoc.202101362] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Erich Kleinpeter
- Chemisches Institut der Universität Potsdam Karl-Liebknecht-Str. 24–25 14476 Potsdam (Golm) Germany E-mail
| | - Andreas Koch
- Chemisches Institut der Universität Potsdam Karl-Liebknecht-Str. 24–25 14476 Potsdam (Golm) Germany E-mail
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9
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Berger RJF, Dimitrova M, Nasibullin RT, Valiev RR, Sundholm D. Integration of global ring currents using the Ampère-Maxwell law. Phys Chem Chem Phys 2022; 24:624-628. [PMID: 34913459 DOI: 10.1039/d1cp05061c] [Citation(s) in RCA: 13] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Magnetically induced ring currents are calculated from the magnetic shielding tensor by employing the Ampère-Maxwell law. The feasibility of the method is demonstrated by integrating the zz component of the shielding tensor along the symmetry axis of highly symmetric ring-shaped aromatic, antiaromatic and nonaromatic molecules. The calculated ring-current strengths agree perfectly with the ones obtained by integrating the current-density flux passing through a plane cutting half the molecular ring. The method can be used in combination with all electronic structure codes capable of calculating nuclear magnetic resonance (NMR) shielding tensors in general points in space. We also show that nucleus independent chemical shifts (NICS) along the symmetry axis are related to the spatial derivative of the strength of the global ring-current along the z axis.
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Affiliation(s)
- Raphael J F Berger
- Chemistry of Materials, Paris-Lodron University of Salzburg, Jakob-Haringerstr. 2A, A-5020 Salzburg, Austria.
| | - Maria Dimitrova
- Chemistry of Materials, Paris-Lodron University of Salzburg, Jakob-Haringerstr. 2A, A-5020 Salzburg, Austria. .,Department of Chemistry, Faculty of Science, P.O. Box 55, A. I. Virtasen aukio 1, FI-00014 University of Helsinki, Finland.
| | | | - Rashid R Valiev
- Department of Chemistry, Faculty of Science, P.O. Box 55, A. I. Virtasen aukio 1, FI-00014 University of Helsinki, Finland. .,Tomsk State University, 36 Lenin Avenue, Tomsk 634050, Russia
| | - Dage Sundholm
- Department of Chemistry, Faculty of Science, P.O. Box 55, A. I. Virtasen aukio 1, FI-00014 University of Helsinki, Finland.
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10
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Sundholm D, Dimitrova M, Berger RJF. Current density and molecular magnetic properties. Chem Commun (Camb) 2021; 57:12362-12378. [PMID: 34726205 DOI: 10.1039/d1cc03350f] [Citation(s) in RCA: 27] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We give an overview of the molecular response to an external magnetic field perturbing quantum mechanical systems. We present state-of-the-art methods for calculating magnetically-induced current-density susceptibilities. We discuss the essence and properties of current-density susceptibilities and how molecular magnetic properties can be calculated from them. We also review the theory of spin-current densities, how relativity affects current densities and magnetic properties. An overview of the magnetic ring-current criterion for aromaticity is given, which has implications on theoretical and experimental research. The recently reported theory of antiaromaticity and how molecular symmetry affects the magnetic response are discussed and applied to closed-shell paramagnetic molecules. The topology of magnetically induced current densities and its consequences for molecular magnetic properties are also presented with twisted and toroidal molecules as examples.
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Affiliation(s)
- Dage Sundholm
- Department of Chemistry, Faculty of Science, FI-00014 University of Helsinki, P.O. Box 55, A. I. Virtasen aukio 1, Finland.
| | - Maria Dimitrova
- Department of Chemistry, Faculty of Science, FI-00014 University of Helsinki, P.O. Box 55, A. I. Virtasen aukio 1, Finland. .,Chemistry of Materials, Paris-Lodron University of Salzburg, Jakob-Haringerstr. 2A, A-5020 Salzburg, Austria
| | - Raphael J F Berger
- Chemistry of Materials, Paris-Lodron University of Salzburg, Jakob-Haringerstr. 2A, A-5020 Salzburg, Austria
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11
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Karadakov PB, VanVeller B. Magnetic shielding paints an accurate and easy-to-visualize portrait of aromaticity. Chem Commun (Camb) 2021; 57:9504-9513. [PMID: 34546260 DOI: 10.1039/d1cc03701c] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Chemists are trained to recognize aromaticity semi-intuitively, using pictures of resonance structures and Frost-Musulin diagrams, or simple electron-counting rules such as Hückel's 4n + 2/4n rule. To quantify aromaticity one can use various aromaticity indices, each of which is a number reflecting some experimentally measured or calculated molecular property, or some feature of the molecular wavefunction, which often has no visual interpretation or may not have direct chemical relevance. We show that computed isotropic magnetic shielding isosurfaces and contour plots provide a feature-rich picture of aromaticity and chemical bonding which is both quantitative and easy-to-visualize and interpret. These isosurfaces and contour plots make good chemical sense as at atomic positions they are pinned to the nuclear shieldings which are experimentally measurable through chemical shifts. As examples we discuss the archetypal aromatic and antiaromatic molecules of benzene and square cyclobutadiene, followed by modern visual interpretations of Clar's aromatic sextet theory, the aromaticity of corannulene and heteroaromaticity.
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Affiliation(s)
- Peter B Karadakov
- Department of Chemistry, University of York, Heslington, York YO10 5DD, UK.
| | - Brett VanVeller
- Department of Chemistry, Iowa State University Ames, IA 50011, USA.
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12
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Abstract
It is shown that the electric dipole- and electric quadrupole–anapole polarizabilities, denoted respectively by fαβ′ and gα,βγ′, and the anapole magnetizability aαβ, are intrinsic properties of the electron cloud of molecules responding to optical fields. fαβ′ is a nonvanishing property of chiral and achiral compounds, whereas aαβ is suitable for enantiomer discrimination of chiral species. They can conveniently be evaluated by numerical integration, employing a formulation complementary to that provided by perturbation theory and relying on the preliminary computation of electronic current density tensors all over the molecular domain. The origin dependence of the dynamic anapolar response is rationalized via related computational techniques employing numerical integration, as well as definitions of molecular property tensors, for example, electric dipole and electric quadrupole polarizabilties and magnetizability. A preliminary application of the theory is reported for the Ra enantiomer of the hydrogen peroxide molecule, evaluating tensor components of electric dipole-anapole polarizability and anapole magnetizability as functions of the dihedral angle ϕ≡∠ H-O-O-H in the range 0∘≤ϕ≤180∘.
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13
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Abstract
A recently developed methodology for calculating, analyzing, and visualizing nuclear magnetic shielding densities is used for studying spatial contributions including ring-current contributions to 1H nuclear magnetic resonance (NMR) chemical shifts of aromatic and anti-aromatic free-base porphyrinoids. Our approach allows a visual inspection of the spatial origin of the positive (shielding) and negative (deshielding) contributions to the nuclear magnetic shielding constants. Diatropic and paratropic current-density fluxes yield both shielding and deshielding contributions implying that not merely the tropicity of the current density determines whether the contribution has a shielding or deshielding character. Instead the shielding or deshielding contribution is determined by the direction of the current-density flux with respect to the studied nucleus.
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14
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Rauhalahti M, Sundholm D, Johansson MP. Magnetically induced ring currents in naphthalene-fused heteroporphyrinoids. Phys Chem Chem Phys 2021; 23:16629-16634. [PMID: 34338707 DOI: 10.1039/d1cp02381k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The magnetically induced current density of an intriguing naphthalene-fused heteroporphyrin has been studied, using the quantum-chemical, gauge-including magnetically induced currents (GIMIC) method. The ring-current strengths and current-density pathways for the heteroporphyrin, its Pd complex, and the analogous quinoline-fused heteroporphyrin provide detailed information about their aromatic properties. The three porphyrinoids have similar current-density pathways and are almost as aromatic as free-base porphyrin. Notably, we show that the global ring current makes a branch at three specific points. Thus, the global current is composed of a total of eight pathways that include 22 π-electrons, with no contributions from 18-electron pathways.
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Affiliation(s)
- Markus Rauhalahti
- University of Helsinki, Department of Chemistry, Faculty of Science, P.O. Box 55 (A.I. Virtanens Plats 1), FI-00014 Helsinki, Finland.
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15
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Lehtola S, Dimitrova M, Fliegl H, Sundholm D. Benchmarking Magnetizabilities with Recent Density Functionals. J Chem Theory Comput 2021; 17:1457-1468. [PMID: 33599491 PMCID: PMC8023670 DOI: 10.1021/acs.jctc.0c01190] [Citation(s) in RCA: 36] [Impact Index Per Article: 12.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2020] [Indexed: 12/21/2022]
Abstract
We have assessed the accuracy of the magnetic properties of a set of 51 density functional approximations, including both recently published and already established functionals. The accuracy assessment considers a series of 27 small molecules and is based on comparing the predicted magnetizabilities to literature reference values calculated using coupled-cluster theory with full singles and doubles and perturbative triples [CCSD(T)] employing large basis sets. The most accurate magnetizabilities, defined as the smallest mean absolute error, are obtained with the BHandHLYP functional. Three of the six studied Berkeley functionals and the three range-separated Florida functionals also yield accurate magnetizabilities. Also, some older functionals like CAM-B3LYP, KT1, BHLYP (BHandH), B3LYP, and PBE0 perform rather well. In contrast, unsatisfactory performance is generally obtained with Minnesota functionals, which are therefore not recommended for calculations of magnetically induced current density susceptibilities and related magnetic properties such as magnetizabilities and nuclear magnetic shieldings. We also demonstrate that magnetizabilities can be calculated by numerical integration of magnetizability density; we have implemented this approach as a new feature in the gauge-including magnetically induced current (GIMIC) method. Magnetizabilities can be calculated from magnetically induced current density susceptibilities within this approach even when analytical approaches for magnetizabilities as the second derivative of the energy have not been implemented. The magnetizability density can also be visualized, providing additional information that is not otherwise easily accessible on the spatial origin of magnetizabilities.
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Affiliation(s)
- Susi Lehtola
- Department
of Chemistry, University of Helsinki, P.O. Box 55, A.I. Virtanens plats
1, FI-00014 University
of Helsinki, Finland
- Molecular
Sciences Software Institute, Blacksburg, Virginia 24061, United States
| | - Maria Dimitrova
- Department
of Chemistry, University of Helsinki, P.O. Box 55, A.I. Virtanens plats
1, FI-00014 University
of Helsinki, Finland
| | - Heike Fliegl
- Institute
of Nanotechnology, KIT, Hermann-von-Helmholtz Platz 1, D-76344 Eggenstein-Leopoldshafen, Germany
| | - Dage Sundholm
- Department
of Chemistry, University of Helsinki, P.O. Box 55, A.I. Virtanens plats
1, FI-00014 University
of Helsinki, Finland
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