1
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Summa FF, Monaco G, Zanasi R. Standard Response Calculation of Electric Dipole Polarizability and Specific Optical Rotation Power Densities. Chemphyschem 2024; 25:e202400203. [PMID: 38747090 DOI: 10.1002/cphc.202400203] [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: 02/26/2024] [Revised: 05/09/2024] [Indexed: 07/10/2024]
Abstract
A time-dependent method has been developed to solve the standard response equation for the calculation of dynamic molecular property densities, endowed with the characteristic of being origin-invariant, entirely in the atomic orbital basis at both HF and DFT level of theory. The method has been tuned in particular for the calculation of origin-independent electric dipole polarizability density and specific rotation power density. Some demonstrations are given for the hexabenzocoronene molecule and the Tröger's base.
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Affiliation(s)
- Francesco F Summa
- Department of Chemistry and Biology "A. Zambelli", University of Salerno, Via Giovanni Paolo II, 132, Fisciano, 84084, SA, Italy
| | - Guglielmo Monaco
- Department of Chemistry and Biology "A. Zambelli", University of Salerno, Via Giovanni Paolo II, 132, Fisciano, 84084, SA, Italy
| | - Riccardo Zanasi
- Department of Chemistry and Biology "A. Zambelli", University of Salerno, Via Giovanni Paolo II, 132, Fisciano, 84084, SA, Italy
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2
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Monaco G, Summa FF, Zanasi R, Lazzeretti P. Electronic Current Density Induced by Uniform Magnetic Fields in Clarenes. Chemistry 2024; 30:e202401167. [PMID: 38656896 DOI: 10.1002/chem.202401167] [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: 03/25/2024] [Revised: 04/19/2024] [Accepted: 04/22/2024] [Indexed: 04/26/2024]
Abstract
Some planar and non-planar clarenes have been studied using maps of magnetically induced quantum-mechanical current density and tools from differential topology to assess their magnetic response in connection with recent results by Du and Wang. Bond current strengths have been computed to estimate quantitative measures. Isosurfaces of the divergence of induced Lorentz force density have been shown to provide useful additional criteria, especially in the case of non-planar clarenes.
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Affiliation(s)
- Guglielmo Monaco
- Department of Chemistry and Biology "A. Zambelli", University of Salerno, via Giovanni Paolo II, 132, Fisciano, 84084, SA, Italy
| | - Francesco F Summa
- Department of Chemistry and Biology "A. Zambelli", University of Salerno, via Giovanni Paolo II, 132, Fisciano, 84084, SA, Italy
| | - Riccardo Zanasi
- Department of Chemistry and Biology "A. Zambelli", University of Salerno, via Giovanni Paolo II, 132, Fisciano, 84084, SA, Italy
| | - Paolo Lazzeretti
- Department of Chemistry and Biology "A. Zambelli", University of Salerno, via Giovanni Paolo II, 132, Fisciano, 84084, SA, Italy
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3
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Badri Z, Foroutan-Nejad C. On the aromaticity of actinide compounds. Nat Rev Chem 2024; 8:551-560. [PMID: 38907002 DOI: 10.1038/s41570-024-00617-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 05/10/2024] [Indexed: 06/23/2024]
Abstract
The chemistry of actinides has flourished since the late 2010s with the synthesis of new actinide complexes and clusters. On the theoretical side, a range of tools is available for the characterization of these heavy element-containing compounds, but discrepancies in the assessment of aromaticity using different tools have led to controversies. In this Perspective, we examine the origin of controversies relating to the aromaticity of metallic compounds, with a focus on actinides. The aromaticity of actinides is important, not because these molecules are numerous or have a special role in catalysis or reactivity, but because this topic pushes theories of aromaticity to their limits. Owing to its reference independence, the magnetic criterion of aromaticity has been the most popular choice for the characterization of the aromaticity of metallic compounds, including actinide compounds. Through examination of several case studies, we show why this criterion might be misleading for metallic species and explain how findings relating to actinide compounds could reshape theories of aromaticity, not just for actinides but perhaps also for well-known hydrocarbons.
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Affiliation(s)
- Zahra Badri
- Institute of Organic Chemistry, Polish Academy of Sciences, Warsaw, Poland
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4
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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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5
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Summa FF, Monaco G, Lazzeretti P, Zanasi R. Electronic current densities and origin-independent property densities induced by optical fields. Phys Chem Chem Phys 2023; 25:25082-25093. [PMID: 37702204 DOI: 10.1039/d3cp01814h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/14/2023]
Abstract
The interaction of a molecule with optical fields is customarily interpreted by means of induced time-dependent electric polarizabilities, magnetizabilities and mixed electric-magnetic polarizabilities. In general, these properties can be rationalized by integrals of density functions formulated in terms of induced charge and current densities. In this perspective, we focus on what has been done so far at the theoretical level, and on what can be expected to be unveiled from the topological study of suitable density functions, endowed with the fundamental requirement of origin invariance. Densities characterized by such a property can be integrated all over the configuration space to obtain electric dipole polarizability and optical rotatory power. Corresponding maps visualize domains mainly involved in the molecular response. The diagonal components of origin-independent density tensor functions that, on integration, yield corresponding electric dipole polarizability tensor of benzene, naphthalene, phenanthrene and ovalene, have been computed, confirming the ubiquitous presence of counter-polarization regions in the proximity of the atomic nuclei. They are associated with toroidal electron currents, induced by time derivative of the electric field of impinging radiation. Electron (de)localization in these systems is readily observed and estimated. The optical rotation density of the carbonyl chromophore is studied in detail. Its essential feature is the separation in quadrants of alternating sign of density about the CO bond. The presence of an extrachromophoric perturbation determines asymmetry in the extension of the quadrant distribution, thus causing optical rotation.
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Affiliation(s)
- Francesco F Summa
- Dipartimento di Chimica e Biologia "A. Zambelli", Università degli Studi di Salerno, via Giovanni Paolo II 132, Fisciano 84084, SA, Italy.
| | - Guglielmo Monaco
- Dipartimento di Chimica e Biologia "A. Zambelli", Università degli Studi di Salerno, via Giovanni Paolo II 132, Fisciano 84084, SA, Italy.
| | - Paolo Lazzeretti
- Dipartimento di Chimica e Biologia "A. Zambelli", Università degli Studi di Salerno, via Giovanni Paolo II 132, Fisciano 84084, SA, Italy.
| | - Riccardo Zanasi
- 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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6
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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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7
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El Bakouri O, Szczepanik DW, Jorner K, Ayub R, Bultinck P, Solà M, Ottosson H. Three-Dimensional Fully π-Conjugated Macrocycles: When 3D-Aromatic and When 2D-Aromatic-in-3D? J Am Chem Soc 2022; 144:8560-8575. [PMID: 35523019 PMCID: PMC9121391 DOI: 10.1021/jacs.1c13478] [Citation(s) in RCA: 19] [Impact Index Per Article: 9.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
![]()
Several fully π-conjugated
macrocycles with puckered or cage-type
structures were recently found to exhibit aromatic character according
to both experiments and computations. We examine their electronic
structures and put them in relation to 3D-aromatic molecules (e.g., closo-boranes) and to 2D-aromatic
polycyclic aromatic hydrocarbons. Using qualitative theory combined
with quantum chemical calculations, we find that the macrocycles explored
hitherto should be described as 2D-aromatic with three-dimensional
molecular structures (abbr. 2D-aromatic-in-3D) and not as truly 3D-aromatic.
3D-aromatic molecules have highly symmetric structures (or nearly
so), leading to (at least) triply degenerate molecular orbitals, and
for tetrahedral or octahedral molecules, an aromatic closed-shell
electronic structure with 6n + 2 electrons. Conversely,
2D-aromatic-in-3D structures exhibit aromaticity that results from
the fulfillment of Hückel’s 4n + 2
rule for each macrocyclic path, yet their π-electron counts
are coincidentally 6n + 2 numbers for macrocycles
with three tethers of equal lengths. It is notable that 2D-aromatic-in-3D
macrocyclic cages can be aromatic with tethers of different lengths, i.e., with π-electron counts different from 6n + 2, and they are related to naphthalene. Finally, we
identify tetrahedral and cubic π-conjugated molecules that fulfill
the 6n + 2 rule and exhibit significant electron
delocalization. Yet, their properties resemble those of analogous
compounds with electron counts that differ from 6n + 2. Thus, despite the fact that these molecules show substantial
π-electron delocalization, they cannot be classified as true
3D-aromatics.
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Affiliation(s)
- Ouissam El Bakouri
- Department of Chemistry - Ångström Laboratory, Uppsala University, Box 523, Uppsala 751 20, Sweden.,Institut de Química Computacional i Catàlisi (IQCC) and Departament de Química, Universitat de Girona, C/ Maria Aurèlia Capmany 6, Girona, Catalonia 17003, Spain
| | - Dariusz W Szczepanik
- Institut de Química Computacional i Catàlisi (IQCC) and Departament de Química, Universitat de Girona, C/ Maria Aurèlia Capmany 6, Girona, Catalonia 17003, Spain.,K. Guminski Department of Theoretical Chemistry, Faculty of Chemistry, Jagiellonian University, Gronostajowa 2, Kraków 30-387, Poland
| | - Kjell Jorner
- Department of Chemistry - Ångström Laboratory, Uppsala University, Box 523, Uppsala 751 20, Sweden
| | - Rabia Ayub
- Department of Chemistry - Ångström Laboratory, Uppsala University, Box 523, Uppsala 751 20, Sweden
| | - Patrick Bultinck
- Department of Chemistry, Ghent University, Krijgslaan 281 S3, Gent 9000, Belgium
| | - Miquel Solà
- Institut de Química Computacional i Catàlisi (IQCC) and Departament de Química, Universitat de Girona, C/ Maria Aurèlia Capmany 6, Girona, Catalonia 17003, Spain
| | - Henrik Ottosson
- Department of Chemistry - Ångström Laboratory, Uppsala University, Box 523, Uppsala 751 20, Sweden
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8
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Persistent Planar Tetracoordinate Carbon in Global Minima Structures of Silicon-Carbon Clusters. ATOMS 2022. [DOI: 10.3390/atoms10010027] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Abstract
Recently, we reported a series of global minima whose structures consist of carbon rings decorated with heavier group 14 elements. Interestingly, these structures feature planar tetracoordinate carbons (ptCs) and result from the replacement of five or six protons (H+) from the cyclopentadienyl anion (C5H5−) or the pentalene dianion (C8H62−) by three or four E2+ dications (E = Si–Pb), respectively. The silicon derivatives of these series are the Si3C5 and Si4C8 clusters. Here we show that ptC persists in some clusters with an equivalent number of C and Si atoms, i.e., Si5C5, Si8C8, and Si9C9. In all these species, the ptC is embedded in a pentagonal C5 ring and participates in a three-center, two-electron (3c-2e) Si-ptC-Si σ-bond. Furthermore, these clusters are π-aromatic species according to chemical bonding analysis and magnetic criteria.
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9
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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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10
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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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11
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López-Estrada O, Selenius E, Zuniga-Gutierrez B, Malola S, Häkkinen H. Cubic aromaticity in ligand-stabilized doped Au superatoms. J Chem Phys 2021; 154:204303. [PMID: 34241155 DOI: 10.1063/5.0050127] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The magnetic response of valence electrons in doped gold-based M@Au8L8 q superatoms (M = Pd, Pt, Ag, Au, Cd, Hg, Ir, and Rh; L = PPh3; and q = 0, +1, +2) is studied by calculating the gauge including magnetically induced currents (GIMIC) in the framework of the auxiliary density functional theory. The studied systems include 24 different combinations of the dopant, total cluster charge, and cluster structure (cubic-like or oblate). The magnetically induced currents (both diatropic and paratropic) are shown to be sensitive to the atomic structure of clusters, the number of superatomic electrons, and the chemical nature of the dopant metal. Among the cubic-like structures, the strongest aromaticity is observed in Pd- and Pt-doped M@Au8L8 0 clusters. Interestingly, Pd- and Pt-doping increases the aromaticity as compared to a similar all-gold eight-electron system Au9L8 +1. With the recent implementation of the GIMIC in the deMon2k code, we investigated the aromaticity in the cubic and butterfly-like M@Au8 core structures, doped with a single M atom from periods 5 and 6 of groups IX-XII. Surprisingly, the doping with Pd and Pt in the cubic structure increases the aromaticity compared to the pure Au case not only near the central atom but encompassing the whole metallic core, following the aromatic trend Pd > Pt > Au. These doped (Pd, Pt)@Au8 nanoclusters show a closed shell 1S21P6 superatom electronic structure corresponding to the cubic aromaticity rule 6n + 2.
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Affiliation(s)
- Omar López-Estrada
- Department of Physics, Nanoscience Center, University of Jyväskylä, FI-40014 Jyväskylä, Finland
| | - Elli Selenius
- Department of Physics, Nanoscience Center, University of Jyväskylä, FI-40014 Jyväskylä, Finland
| | - Bernardo Zuniga-Gutierrez
- Departamento de Química, Universidad de Guadalajara, CUCEI, Blvd. Marcelino García Barragán 1421, C. P. 44430 Guadalajara, Jalisco, Mexico
| | - Sami Malola
- Department of Physics, Nanoscience Center, University of Jyväskylä, FI-40014 Jyväskylä, Finland
| | - Hannu Häkkinen
- Department of Physics, Nanoscience Center, University of Jyväskylä, FI-40014 Jyväskylä, Finland
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12
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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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13
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Jinger R, Fliegl H, Bast R, Dimitrova M, Lehtola S, Sundholm D. Spatial Contributions to Nuclear Magnetic Shieldings. J Phys Chem A 2021; 125:1778-1786. [PMID: 33605721 PMCID: PMC8023705 DOI: 10.1021/acs.jpca.0c10884] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/05/2020] [Revised: 02/05/2021] [Indexed: 01/09/2023]
Abstract
We develop a methodology for calculating, analyzing, and visualizing nuclear magnetic shielding densities which are calculated from the current density via the Biot-Savart relation. Atomic contributions to nuclear magnetic shielding constants can be estimated within our framework with a Becke partitioning scheme. The new features have been implemented in the GIMIC program and are applied in this work to the study of the 1H and 13C nuclear magnetic shieldings in benzene (C6H6) and cyclobutadiene (C4H4). The new methodology allows a visual inspection of the spatial origins of the positive (shielding) and negative (deshielding) contributions to the nuclear magnetic shielding constant of a single nucleus, something which has not been hitherto easily accomplished. Analysis of the shielding densities shows that diatropic and paratropic current-density fluxes yield both shielding and deshielding contributions, as the shielding or deshielding is determined by the direction of the current-density flux with respect to the studied nucleus instead of the tropicity. Becke partitioning of the magnetic shieldings shows that the magnetic shielding contributions mainly originate from the studied atom and its nearest neighbors, confirming the localized character of nuclear magnetic shieldings.
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Affiliation(s)
- Rahul
Kumar Jinger
- Indian
Institute of Science Education and Research, Dr. Homi Bhabha Road, Pashan, Pune 411008, India
| | - Heike Fliegl
- Karlsruhe
Institute of Technology, Institute of Nanotechnology, Hermann-von-Helmholtz Platz 1, D-76344 Eggenstein-Leopoldshafen, Germany
| | - Radovan Bast
- Department
Information Technology, UiT Arctic University
Norway, Tromsø, Norway
| | - Maria Dimitrova
- Department
of Chemistry, Faculty of Science, University
of Helsinki, P.O. Box 55, FI-00014 Helsinki, Finland
| | - Susi Lehtola
- Department
of Chemistry, Faculty of Science, University
of Helsinki, P.O. Box 55, FI-00014 Helsinki, Finland
- Molecular
Sciences Software Institute, Blacksburg, Virginia 24061, United States
| | - Dage Sundholm
- Department
of Chemistry, Faculty of Science, University
of Helsinki, P.O. Box 55, FI-00014 Helsinki, Finland
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14
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Radenković S, Đorđević S. Relating nucleus independent chemical shifts with integrated current density strengths. Phys Chem Chem Phys 2021; 23:11240-11250. [PMID: 33949527 DOI: 10.1039/d1cp00784j] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Indices based on the nucleus independent chemical shift (NICS) are the most frequently used in analysis of magnetic aromaticity. The magnetically induced current density, on the other hand, is a key concept in defining magnetic aromaticity. The integrated current strength (current strength susceptibility) was found to be a very useful tool in aromaticity studies. There is widely accepted notion that the properly chosen NICS-based index can provide information on the current density strength and direction in a molecule of interest. In this work, a detailed numerical testing of the relationship between the integrated bond current strength and the most employed NICS indices was performed for a set of 43 monocyclic aromatic molecules. Based on the statistical data analysis, the relationship between the bond current strength and its π and σ electron components, on one side, and the isotropic NICS (NICSiso and NICSπ,iso) and zz-component of the NICS tensor (NICSzz and NICSπ,zz), on the other side, was examined. It was found that between the NICSπ,zz(1) and π-electron bond current strenghts there is very good linear correlation. Quite surprisingly, it was revealed that the NICSiso(1) and NICSzz(1) are not correlated with the π electron bond current strengths. On the other hand, a reasonably good linear correlation was found between the NICSzz(1) and total bond current strengths.
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Affiliation(s)
- Slavko Radenković
- Faculty of Science, University of Kragujevac, P. O. Box 60, 34000 Kragujevac, Serbia.
| | - Slađana Đorđević
- Faculty of Science, University of Kragujevac, P. O. Box 60, 34000 Kragujevac, Serbia.
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15
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Lazzeretti P. Cubic magnetic response of diamagnetic molecules via third-order electronic current density. J Chem Phys 2020; 153:234112. [PMID: 33353312 DOI: 10.1063/5.0029595] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
An approach to nonlinear magnetic properties of a diamagnetic molecule in the presence of a strong homogeneous magnetic field B is proposed, introducing the notion of third-order electronic current density and associated fourth-rank current density tensors via a perturbation expansion. It is shown that cubic magnetic response properties, e.g., fourth-rank magnetizability and fourth-rank nuclear magnetic shielding, can be expressed by relationships alternative to those arrived through perturbation theory by means of third-order current density. A sum rule, providing a condition in integral form for electron charge conservation to the third order in B, has been obtained.
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Affiliation(s)
- Paolo Lazzeretti
- Istituto di Struttura della Materia Consiglio Nazionale delle Ricerche, Via del Fosso del Cavaliere 100, 00133 Roma, Italy
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16
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Monaco G, Summa FF, Zanasi R. Program Package for the Calculation of Origin-Independent Electron Current Density and Derived Magnetic Properties in Molecular Systems. J Chem Inf Model 2020; 61:270-283. [PMID: 33347314 DOI: 10.1021/acs.jcim.0c01136] [Citation(s) in RCA: 30] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We present SYSMOIC, a program package for the calculation of the origin-independent current density induced at first order by an external magnetic field in planar and nonplanar molecular systems. Origin independence is obtained adopting the continuous transformation of the origin of the current density method, implemented at both density functional theory (DFT) and Hartree-Fock (HF) levels. Expansion coefficients for perturbed and unperturbed molecular orbitals, over basis sets containing up to m-type Gaussian functions, can be calculated by the package itself or obtained from a Gaussian calculation. A number of different functionalities presented so far in the literature that are connected to the induced current, such as current density maps for any orientation of the inducing magnetic field, net bond current strengths, stagnation graphs, magnetic shielding densities, vorticities, and anisotropies, are now made available all together in a single multiplatform package installation.
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Affiliation(s)
- Guglielmo Monaco
- Dipartimento di Chimica e Biologia "A. Zambelli", Università degli Studi di Salerno, via Giovanni Paolo II 132, Fisciano 84084 SA, Italy
| | - Francesco F Summa
- Dipartimento di Chimica e Biologia "A. Zambelli", Università degli Studi di Salerno, via Giovanni Paolo II 132, Fisciano 84084 SA, Italy
| | - Riccardo Zanasi
- 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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17
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Lazzeretti P. Tests of accuracy for computed magnetic properties via off-diagonal hypervirial relations. J Chem Phys 2020; 153:214108. [PMID: 33291908 DOI: 10.1063/5.0035563] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Most of the methods presently available to investigate the molecular magnetic response work extremely well for the computation of properties, such as magnetizability and nuclear magnetic shielding, but they provide insufficiently accurate current density maps, in that they do not guarantee exact conservation, leading to unphysical features in maps. The present study starts from the results obtained by Epstein and Sambe and moves forward to generalize them. An off-diagonal hypervirial relationship, connecting the matrix elements of a given differentiable function of position f(r) to its derivatives ∇f(r), via the anticommutator ∇αf,p^α + with the canonical momentum operator p^, has first been proven. Afterward, this relationship is applied to show that the equations proposed by Sambe to check the quality and conservation of computed electronic current densities can be obtained as particular cases of this general theorem, with a substantial gain in computational efficiency. Connections with previous work by Arrighini, Maestro, and Moccia are outlined, and the implications that hint at future work are discussed.
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Affiliation(s)
- Paolo Lazzeretti
- Istituto di Struttura della Materia, Consiglio Nazionale delle Ricerche, Via del Fosso del Cavaliere 100, 00133 Roma, Italy
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18
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Monaco G, Zanasi R. The molecular electronic structure revealed by the magnetically induced Lorentz force density. J Chem Phys 2020; 153:104114. [DOI: 10.1063/5.0021928] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022] Open
Affiliation(s)
- Guglielmo Monaco
- Dipartimento di Chimica e Biologia “A. Zambelli,” Università di Salerno, Via G. Paolo II, 132, 84084 Fisiciano, Italy
| | - Riccardo Zanasi
- Dipartimento di Chimica e Biologia “A. Zambelli,” Università di Salerno, Via G. Paolo II, 132, 84084 Fisiciano, Italy
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19
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Lazzeretti P. Static and optical anapole magnetizabilities and polarizabilities. J Chem Phys 2020; 153:074102. [DOI: 10.1063/5.0019937] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Paolo Lazzeretti
- Istituto di Struttura della Materia, Consiglio Nazionale delle Ricerche, Via del Fosso del Cavaliere 100, 00133 Roma, Italy
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20
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Komorovsky S, Jakubowska K, Świder P, Repisky M, Jaszuński M. NMR Spin–Spin Coupling Constants Derived from Relativistic Four-Component DFT Theory—Analysis and Visualization. J Phys Chem A 2020; 124:5157-5169. [DOI: 10.1021/acs.jpca.0c02807] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Stanislav Komorovsky
- Institute of Inorganic Chemistry, Slovak Academy of Sciences, Dubravska cesta 9, Bratislava 845 36, Slovakia
| | | | - Paweł Świder
- Institute of Organic Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, Warszawa 01-224, Poland
| | - Michal Repisky
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, UiT − The Arctic University of Norway, Tromsø N-9037, Norway
| | - Michał Jaszuński
- Institute of Organic Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, Warszawa 01-224, Poland
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21
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Pelloni S, Lazzeretti P. Anisotropy of the vorticity tensor as a magnetic indicator of aromaticity. Phys Chem Chem Phys 2020; 22:1299-1305. [DOI: 10.1039/c9cp05563k] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The vorticity vector of the current density JB, induced in the electron cloud of a molecule by a magnetic field B, is defined by VB = ∇ × JB.
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Affiliation(s)
- S. Pelloni
- Istituto d'istruzione superiore Francesco Selmi
- 41126 Modena
- Italy
| | - P. Lazzeretti
- Istituto di Struttura della Materia
- Consiglio Nazionale delle Ricerche
- 00133 Roma
- Italy
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22
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Lazzeretti P. Continuity equations for electron charge densities and current densities induced in molecules by electric and magnetic fields. J Chem Phys 2019; 151:114108. [PMID: 31542030 DOI: 10.1063/1.5124250] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Paolo Lazzeretti
- Istituto di Struttura della Materia, Consiglio Nazionale delle Ricerche, Via del Fosso del Cavaliere 100, 00133 Roma, Italy
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23
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Martins FA, Pires FC, da Cunha EFF, Freitas MP. Does induced current density explain the C-H and C-F Perlin effects? Phys Chem Chem Phys 2019; 21:18622-18628. [PMID: 31414084 DOI: 10.1039/c9cp02558h] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Spin-spin coupling constant (SSCC) data may be useful in providing information on the stereochemistry and intramolecular interactions in molecules. One-bond C-H and C-F SSCCs (1JCH and 1JCF) are amongst the most important NMR parameters used to study the structure of alicyclic six-membered rings, because the Perlin effect, defined as 1JCHeq > 1JCHax, and the fluorine Perlin-like effect, defined as |1JCFeq| > |1JCFax|, are in wide currency to probe the conformations of these compounds. The origin of these effects has been usually attributed either to dipolar interactions or hyperconjugation, while the induced current density (ICD) has been recently correlated to the magnetic shielding tensors in some six-membered ring compounds, and then used to explain the Perlin effect. Accordingly, this work reports an analysis of the ICD as a descriptor of 1JCH and 1JCF in a series of six-membered rings to find out the role of the ICD in the conventional and fluorine Perlin effect. The atoms in molecules (AIM) magnetic responses obtained from density functional theory (DFT) calculations for the studied compounds did not show any relationship of the first-order electronic current density (ΔJ(1)) with the calculated Δ1JCHax-eq and Δ1JCFax-eq values. Consequently, the title effects cannot be precisely explained by ICD. Nevertheless, an interesting relationship between ΔJ(1) and Δdelocalization involving σCH* orbitals is observed.
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Affiliation(s)
- Francisco A Martins
- Department of Chemistry, Federal University of Lavras, 37200-000, Lavras, MG, Brazil.
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24
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Barquera‐Lozada JE. Vorticity: Simplifying the analysis of the current density. J Comput Chem 2019; 40:2602-2610. [DOI: 10.1002/jcc.26018] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2019] [Revised: 05/23/2019] [Accepted: 06/16/2019] [Indexed: 01/24/2023]
Affiliation(s)
- José E. Barquera‐Lozada
- Instituto de Química, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, Coyoacán Ciudad de México 04510 Mexico
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25
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Lazzeretti P. Frequency-dependent current density tensors as density functions of dynamic polarizabilities. J Chem Phys 2019; 150:184117. [PMID: 31091911 DOI: 10.1063/1.5097578] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Relationships accounting for contributions to the first-order charge density ρ(1) and current density J(1), induced in the electrons of a molecule by a monochromatic plane wave, have been obtained via time-dependent quantum mechanical perturbation theory. Their gauge invariance and invariance in passive translations of the coordinate system have been demonstrated (i) within the (long wavelengths) electric dipole approximation, in which only the electric field contributions to these densities are required, and (ii) within the electric quadrupole approximation, in which nonseparable terms provided by the magnetic field and by the electric field gradient, assumed uniform over the molecular domain, are needed. It is shown that the physical meaning of current density tensors depending on the frequency ω of the monochromatic wave shone on the molecule, and corresponding to derivatives of the current density J(1)(r, ω) with respect to components of the perturbing fields, is that of property density. Therefore, frequency-dependent current density tensors can be interpreted as the integrand function in 3d-space integrals defining dynamic molecular response tensors, e.g., electric dipole, mixed electric dipole-magnetic dipole, and electric dipole-quadrupole polarizabilites. Plots of current density tensors are expected to provide important information on the molecular domains giving dominant contributions to these properties.
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Affiliation(s)
- Paolo Lazzeretti
- Istituto di Struttura Della Materia, Consiglio Nazionale Delle Ricerche, Via Del Fosso Del Cavaliere, 100, 00133 Roma, Italy
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26
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Monaco G, Zanasi R. Delocalization energy retrieved from the current density tensor. Phys Chem Chem Phys 2019; 21:11564-11568. [DOI: 10.1039/c9cp00117d] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The anisotropy of the magnetically induced current density tensor can be computed by its original formulation, known in the literature as ACID, or by its revised definition, AACID, which takes into account the asymmetric nature of the tensor. In polycyclic aromatic hydrocarbons, the excess of the integrated value of AACID over that computed for isolated ethylenes correlate with the Hückel delocalization energy.
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Affiliation(s)
- Guglielmo Monaco
- Dipartimento di Chimica e Biologia “A. Zambelli”
- Università degli Studi di Salerno
- Fisciano 84084
- Italy
| | - Riccardo Zanasi
- Dipartimento di Chimica e Biologia “A. Zambelli”
- Università degli Studi di Salerno
- Fisciano 84084
- Italy
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27
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Lazzeretti P. Gauge invariance and origin independence of electronic charge density and current density induced by optical fields. J Chem Phys 2018; 149:154106. [PMID: 30342457 DOI: 10.1063/1.5052352] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Expressions for the first-order polarization charge density ρ (1) and current density J (1) induced in a molecule by a monochromatic plane wave, obtained by time-dependent quantum mechanical perturbation theory, have been investigated to assess their gauge invariance and independence of the coordinate system in passive and active translations. The conditions arrived at show that, within the (long wavelengths) dipole approximation, only the electric contributions to these densities are needed to rationalize the phenomenology. To the next higher quadrupole approximation, assuming that the magnetic field and the electric field gradient are uniform over the molecular dimensions, corresponding contributions to ρ (1) and J (1) are considered. It has been found that total densities are independent of the origin, whereas the contributions from electric and magnetic fields are not separately invariant. A magnetic contribution to J (1), which is by itself origin independent, can be defined by means of an approach based on continuous translation of the origin of the coordinate system.
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Affiliation(s)
- Paolo Lazzeretti
- Istituto di Struttura della Materia Consiglio Nazionale delle Ricerche, Via del Fosso del Cavaliere 100, 00133 Roma, Italy
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29
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Rabanal-León WA, Vásquez-Espinal A, Yañez O, Pino-Rios R, Arratia-Pérez R, Alvarez-Thon L, Torres-Vega JJ, Tiznado W. Aromaticity of [M3(µ-X)3X6]0/2-(M = Re and Tc, X = Cl, Br, I) Clusters Confirmed by Ring Current Analysis and Induced Magnetic Field. Eur J Inorg Chem 2018. [DOI: 10.1002/ejic.201800339] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Walter A. Rabanal-León
- Departamento de Ciencias Químicas; Facultad de Ciencias Exactas; Universidad Andres Bello; Av. República 275, Santiago, Chile República 275 Santiago Chile
| | - Alejandro Vásquez-Espinal
- Departamento de Física Aplicada; Centro de Investigación y de Estudios Avanzados; Unidad Mérida; Km 6 Antigua carretera a Progreso, Apdo. Postal 73 97310 Cordemex México
| | - Osvaldo Yañez
- Departamento de Ciencias Químicas; Facultad de Ciencias Exactas; Universidad Andres Bello; Av. República 275, Santiago, Chile República 275 Santiago Chile
| | - Ricardo Pino-Rios
- Departamento de Ciencias Químicas; Facultad de Ciencias Exactas; Universidad Andres Bello; Av. República 275, Santiago, Chile República 275 Santiago Chile
| | - Ramiro Arratia-Pérez
- Universidad Andrés Bello; Doctorado en Fisicoquímica Molecular; República 275 Santiago Chile
| | - Luis Alvarez-Thon
- Facultad de Ingeniería; Universidad Central de Chile; Toesca 1783 Santiago Chile
| | - Juan J. Torres-Vega
- Facultad de Ciencias Físicas; Universidad Nacional Mayor de San Marcos; P.O. Box 14-0149 Lima Perú
| | - William Tiznado
- Departamento de Ciencias Químicas; Facultad de Ciencias Exactas; Universidad Andres Bello; Av. República 275, Santiago, Chile República 275 Santiago Chile
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Janda T, Foroutan‐Nejad C. Why is Benzene Unique? Screening Magnetic Properties of C6H6Isomers. Chemphyschem 2018; 19:2357-2363. [DOI: 10.1002/cphc.201800364] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2018] [Indexed: 11/08/2022]
Affiliation(s)
- Tomáš Janda
- Department of Chemistry, Faculty of ScienceMasaryk University Kamenice 5, CZ – 62500 Brno Czech Republic
- Institute of Chemistry and Technology of Macromolecular Materials, Faculty of Chemical TechnologyUniversity of Pardubice
| | - Cina Foroutan‐Nejad
- CEITEC – Central European Institute of Technology, Masaryk University Kamenice 5, CZ – 62500 Brno Czech Republic
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31
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Monaco G, Zanasi R. AACID: Anisotropy of the Asymmetric Magnetically Induced Current Density Tensor. J Phys Chem A 2018; 122:4681-4686. [DOI: 10.1021/acs.jpca.8b03663] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Guglielmo Monaco
- Dipartimento di Chimica e Biologia “A. Zambelli”, Università degli Studi di Salerno, Via Giovanni Paolo II 132, Fisciano 84084, SA Italy
| | - Riccardo Zanasi
- 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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