Integration of global ring currents using the Ampère–Maxwell law

Berger, Raphael J. F.; Dimitrova, Maria; Nasibullin, Rinat T.; Valiev, Rashid R.; Sundholm, Dage

doi:10.1039/d1cp05061c

Cited by 22 publications

(37 citation statements)

References 46 publications

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“…Integrating the zz component of the magnetic shielding tensor along the symmetry axis in the middle of the ring yields the strength of the magnetically induced ring current according to Ampère–Maxwell’s law. 53 The ring-current strength calculated at the BHandHLYP and CASSCF levels for the singlet state of C 11 agree, whereas the CASSCF calculation suggests a stronger ring current for the triplet state than that obtained at the BHandHLYP level. Both levels of theory suggest that the singlet and triplet states of C 13 are antiaromatic.…”

Section: Resultsmentioning

confidence: 78%

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Odd-Number Cyclo[n]Carbons Sustaining Alternating Aromaticity

et al. 2022

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Cyclo[ n ]carbons ( n = 5, 7, 9, ..., 29) composed from an odd number of carbon atoms are studied computationally at density functional theory (DFT) and ab initio complete active space self-consistent field (CASSCF) levels of theory to get insight into their electronic structure and aromaticity. DFT calculations predict a strongly delocalized carbene structure of the cyclo[ n ]carbons and an aromatic character for all of them. In contrast, calculations at the CASSCF level yield geometrically bent and electronically localized carbene structures leading to an alternating double aromaticity of the odd-number cyclo[ n ]carbons. CASSCF calculations yield a singlet electronic ground state for the studied cyclo[ n ]carbons except for C 25 , whereas at the DFT level the energy difference between the lowest singlet and triplet states depends on the employed functional. The BHandHLYP functional predicts a triplet ground state of the larger odd-number cyclo[ n ]carbons starting from n = 13. Current-density calculations at the BHandHLYP level using the CASSCF-optimized molecular structures show that there is a through-space delocalization in the cyclo[ n ]carbons. The current density avoids the carbene carbon atom, leading to an alternating double aromaticity of the odd-number cyclo[ n ]carbons satisfying the antiaromatic [4k+1] and aromatic [4k+3] rules. C 11 , C 15 , and C 19 are aromatic and can be prioritized in future synthesis. We predict a bond-shift phenomenon for the triplet state of the cyclo[ n ]carbons leading to resonance structures that have different reactivity toward dimerization.

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Section: Resultsmentioning

confidence: 78%

“… 52 The ring-current strengths were then obtained at the CASSCF level by integrating the zz component of the shielding tensor along the symmetry axis in the middle of the ring using the Ampère–Maxwell’s law. 53 …”

Section: Computational Detailsmentioning

confidence: 99%

Odd-Number Cyclo[n]Carbons Sustaining Alternating Aromaticity

et al. 2022

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“…As we have shown previously, 7 and since B ind is vanishing at infinity in z and y direction, the total current flux, Φ ℓ 1 , of the outer vortex can be obtained from the line integral…”

Section: Resultsmentioning

confidence: 85%

“…We have recently reported some progress on the quantitative characterization of the current-density field 7 from the secondary magnetic field that it induces which is better known as nucleus-independent chemical shifts (NICS) or also as induced magnetic field B ind (the latter with an opposite sign as compared to NICS). 8 The obtained data can be used in arguments about the aromatic or antiaromatic nature of a compound.…”

Section: Introductionmentioning

confidence: 99%

“…For the quantification of the molecular current density, one is typically interested in its flux, Φ, through a particular surface, S , chosen according to chemical intuition or other demands or model ideas, such as the "ring-current" model for molecular systems consisting of one or more rings. 2 The idea underlying our recent work 7 was to apply the integral form of the Ampère-Maxwell law instead of evaluating a surface integral of J. The line integral of B ind (the induced magnetic field), over the boundary line ∂ S of the surface S is defined by…”

Section: Introductionmentioning

confidence: 99%

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The Oriented and Flux-Weighted Current Density Stagnation Graph of LiH

Berger

Dimitrova

2022

Preprint

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A scheme is introduced to quantitatively analyze the magnetically induced molecular current density vector field J. After determining the set of zero points of J, which is called its stagnation graph (SG), the line integrals -1/mu_0 \int_li B.dl along all edges of the connected subset of the SG are determined. The edges are oriented such that all line integrals are non-negative and they are weighted with the resultants. An oriented flux-weighted (current density) stagnation graph (OFW-SG) is obtained. Since J is in the exact theoretical limit divergence free and due to the topological characteristics of such vector fields the flux of all separate vortices and neighbouring vortex combinations can be determined by adding the weights of cyclic subsets of edges of the OFW-SG. The procedure is exemplified by the case of LiH for a perpendicular and weak homogeneous external magnetic field B.

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[GeRu₆(CO)₁₈HI]: A Germanium‐Centered Ruthenium Carbonyl Cluster with Aromatic Ring Current

Wolf,

Köppe,

Treptow

et al. 2024

Advanced Science

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The carbonyl cluster compound [GeRu6(CO)18HI] is unique in regard to its structure and bonding with a GeRu6 cluster core, a planar GeRu4HI unit, extensive multi‐center bonding, and an aromatic ring current similar to benzene (9‐10 nA T−1). The open‐shell cluster core is a Ge‐centered five‐membered Ru4(Ru2) ring with CO ligands and an additional H and I atom, each bridging two Ru atoms on opposite sides of the cluster core. The compound is prepared at 130 °C in a weakly‐coordinating ionic liquid.

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Integration of global ring currents using the Ampère–Maxwell law

Abstract: Magnetically induced ring current are calculated from the magnetic shielding tensor by employing the Ampére-Maxwell law. The feasibility of the method is demonstrated by integrating the zz component of the...

Cited by 22 publications

References 46 publications

Odd-Number Cyclo[n]Carbons Sustaining Alternating Aromaticity

Odd-Number Cyclo[n]Carbons Sustaining Alternating Aromaticity

The Oriented and Flux-Weighted Current Density Stagnation Graph of LiH

[GeRu₆(CO)₁₈HI]: A Germanium‐Centered Ruthenium Carbonyl Cluster with Aromatic Ring Current

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Integration of global ring currents using the Ampère–Maxwell law

Abstract: Magnetically induced ring current are calculated from the magnetic shielding tensor by employing the Ampére-Maxwell law. The feasibility of the method is demonstrated by integrating the zz component of the...

Cited by 22 publications

References 46 publications

Odd-Number Cyclo[n]Carbons Sustaining Alternating Aromaticity

Odd-Number Cyclo[n]Carbons Sustaining Alternating Aromaticity

The Oriented and Flux-Weighted Current Density Stagnation Graph of LiH

[GeRu6(CO)18HI]: A Germanium‐Centered Ruthenium Carbonyl Cluster with Aromatic Ring Current

Contact Info

Product

Resources

About

[GeRu₆(CO)₁₈HI]: A Germanium‐Centered Ruthenium Carbonyl Cluster with Aromatic Ring Current