Computational study of basis set and electron correlation effects on anapole magnetizabilities of chiral molecules

Zarycz, Natalia; Provasi, Patricio F.; Pagola, Gabriel Ignacio; Ferraro, Marta B.; Pelloni, Stefano; Lazzeretti, Paolo

doi:10.1002/jcc.24369

Cited by 18 publications

(39 citation statements)

References 38 publications

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“…Tensor operators are expressed specifying the components, for example, for the second‐rank tensor operator corresponding to the magnetic quadrupole, 52,53

{\overset{true^}{m}}_{αβ} = - \frac{e}{6 m_{e}} \sum_{k = 1}^{n} {({\overset{l}{true}}_{α} r_{β} + r_{β} {\overset{l}{true}}_{α})}_{k},

and for its antisymmetric part, which defines the parity‐odd, time‐odd, anapole vector operator, 53

{\overset{true^}{a}}_{α} = - \frac{1}{2} ɛ_{αβγ} {\overset{true^}{m}}_{βγ} = \frac{e}{6 m_{e}} \sum_{k = 1}^{n} {[(r^{2} δ_{italicαβ} - r_{α} r_{β}) {\overset{p}{true}}_{β} + iℏ r_{α}]}_{k} .

…”

Section: Outline Of Notation and Theoretical Methodsmentioning

confidence: 99%

“…The static anapole magnetizability a αβ is a nonsymmetric parity‐odd, time‐even, second‐rank tensor, expressed as the sum of paramagnetic and diamagnetic contributions, 51,53–58

a_{αβ} = a_{αβ}^{p} + a_{αβ}^{d},

a_{αβ}^{p} = \frac{1}{ℏ} \sum_{j \neq a} \frac{2}{ω_{italicja}} ℜ ((), (〈〉||, a, {\overset{a}{true}}_{α}, j) (〈〉||, j, {\overset{m}{true}}_{β}, a)),

a_{αβ}^{d} = \frac{e^{2}}{12 m_{e}} ɛ_{αβγ} (〈〉||, a, \sum_{k = 1}^{n} {(r^{2} r_{γ})}_{k}, a) .

…”

Section: Outline Of Notation and Theoretical Methodsmentioning

confidence: 99%

“…In a translation of coordinate system represented by the shift of origin

r^{'} \to r^{''} = r^{'} + bold-italicd,

the anapole magnetizability transforms according to the relation

a_{γδ} ((), {bold-italicr}^{''}) = a_{γδ} ((), {bold-italicr}^{'}) + \frac{1}{2} ɛ_{αβγ} ξ_{δα} d_{β},

where ξ δα is the molecular magnetizability. Thus, according to Equation (), diagonal components and trace of () are origin independent in the principal axis system of the symmetric ξ αβ tensor 53 …”

Section: Outline Of Notation and Theoretical Methodsmentioning

confidence: 99%

“…A large uncontracted (13s10p5d2f/11s7p4d) basis set, previously tested for predicting anapole magnetizabilities of other chiral molecules, 53 has been employed to compute a αβ and

κ_{αβ}^{'}

for a series of molecular conformations corresponding to different values of the HX–XH dihedral angle, with X = N, B, and C, using the DALTON code 77…”

Section: Computationsmentioning

confidence: 99%

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Physical achirality in geometrically chiral rotamers of hydrazine and boranylborane molecules

et al. 2021

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The diagonal components and the trace of tensors which account for chiroptical response of the hydrazine molecule N2H4, that is, static anapole magnetizability and frequency‐dependent electric dipole‐magnetic dipole polarisability, are a function of the ϕ≡∠ H─N─N─H dihedral angle. They vanish for symmetry reasons at ϕ = 0° and ϕ = 180°, corresponding respectively to C2v and C2h point group symmetries, that is, cis and trans conformers characterized by the presence of molecular symmetry planes. Nonetheless, vanishing diagonal components have been observed also in the proximity of ∠ H─N─N─H = 90°, in which the point group symmetry is C2 and hydrazine is unquestionably chiral. In the boranylborane molecule B2H4, assuming the B─B bond in the y direction, the ayy component of the anapole magnetizability tensor approximately vanishes for dihedral angles ∠ H─B─B─H corresponding to chiral rotamers which belong to D2 symmetry. Such anomalous effects have been ascribed to physical achirality of these conformers, that is, to their inability to sustain electronic current densities inducing either anapole moments, or electric and magnetic dipole moments, about the chiral axis connecting heavier atoms, as well as perpendicular directions. In other terms, the structure of certain geometrically chiral rotamers may be such that neither toroidal nor helical flow, which determine chiroptical phenomenology, can take place in the presence of perturbing fields parallel or orthogonal to the chiral axis.

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“…Tensor operators are expressed specifying the components, for example, for the second‐rank tensor operator corresponding to the magnetic quadrupole, 52,53

{\overset{true^}{m}}_{αβ} = - \frac{e}{6 m_{e}} \sum_{k = 1}^{n} {({\overset{l}{true}}_{α} r_{β} + r_{β} {\overset{l}{true}}_{α})}_{k},

and for its antisymmetric part, which defines the parity‐odd, time‐odd, anapole vector operator, 53

{\overset{true^}{a}}_{α} = - \frac{1}{2} ɛ_{αβγ} {\overset{true^}{m}}_{βγ} = \frac{e}{6 m_{e}} \sum_{k = 1}^{n} {[(r^{2} δ_{italicαβ} - r_{α} r_{β}) {\overset{p}{true}}_{β} + iℏ r_{α}]}_{k} .

…”

Section: Outline Of Notation and Theoretical Methodsmentioning

confidence: 99%

“…The static anapole magnetizability a αβ is a nonsymmetric parity‐odd, time‐even, second‐rank tensor, expressed as the sum of paramagnetic and diamagnetic contributions, 51,53–58

a_{αβ} = a_{αβ}^{p} + a_{αβ}^{d},

a_{αβ}^{p} = \frac{1}{ℏ} \sum_{j \neq a} \frac{2}{ω_{italicja}} ℜ ((), (〈〉||, a, {\overset{a}{true}}_{α}, j) (〈〉||, j, {\overset{m}{true}}_{β}, a)),

a_{αβ}^{d} = \frac{e^{2}}{12 m_{e}} ɛ_{αβγ} (〈〉||, a, \sum_{k = 1}^{n} {(r^{2} r_{γ})}_{k}, a) .

…”

Section: Outline Of Notation and Theoretical Methodsmentioning

confidence: 99%

“…In a translation of coordinate system represented by the shift of origin

r^{'} \to r^{''} = r^{'} + bold-italicd,

the anapole magnetizability transforms according to the relation

a_{γδ} ((), {bold-italicr}^{''}) = a_{γδ} ((), {bold-italicr}^{'}) + \frac{1}{2} ɛ_{αβγ} ξ_{δα} d_{β},

Section: Outline Of Notation and Theoretical Methodsmentioning

confidence: 99%

“…A large uncontracted (13s10p5d2f/11s7p4d) basis set, previously tested for predicting anapole magnetizabilities of other chiral molecules, 53 has been employed to compute a αβ and

κ_{αβ}^{'}

for a series of molecular conformations corresponding to different values of the HX–XH dihedral angle, with X = N, B, and C, using the DALTON code 77…”

Section: Computationsmentioning

confidence: 99%

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Physical achirality in geometrically chiral rotamers of hydrazine and boranylborane molecules

et al. 2021

Self Cite

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“…It is an important descriptor to study chemical reactivity, stability and aromaticity of different atoms and molecules. [9][10][11][12][13][14] Dynamics of reactions have also been studied for molecules in confinement using magnetizability. 15 This property is of multidisciplinary interest and has extensive applications in the realm of physical, biological, engineering and materials science such as organic electronics, 16 magnetically labelled cells, drugs and therapeutic agents, 17 magnetic flux concentrators, 18 magnetizable elastomers, 19 bionanocomposites, 20 magnetic immunoadsorbents, 21 magnetic nanoparticles/ nanofibres 17 and so on besides its use in general chemical science.…”

Section: Introductionmentioning

confidence: 99%

n the Validity of Minimum Magnetizability Principle in Chemical Reactions

Tandon

Chakraborty

Suhag

2021

ACSi

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A new principle known as Minimum Magnetizability Principle has recently been introduced in the context of Density Functional Theory. In order to validate this principle, changes in the magnetizability (Δξ) and its cube-root (Δξ1/3) are computed at B3LYP/LanL2DZ level of theory for some elementary chemical reactions. The principle is found to be valid for 77% of reactions under study. It is observed that the molecules with the lowest sum of ξ or ξ1/3 are generally the most stable. The principle fails to work in the presence of hard species. A comparative study is also made with change in hardness (Δη), electrophilicity index (Δω), polarizability (Δα) and their cube-roots (Δη1/3, Δω1/3, Δα1/3). It is observed that the Minimum Magnetizability Principle is nearly as reliable as Minimum Electrophilicity Principle. It appears that this principle could be helpful in predicting the direction of diverse reactions as well as stable geometrical arrangements.

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On the axial chirality of leucoindigo

et al. 2023

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The diagonal components and the trace of two tensors which account for chiroptical response of the leucoindigo molecule C 16 H 12 N 2 O 2 that is, static anapole magnetizability, and dynamic electric dipole-magnetic dipole polarisability depending on the frequency of impinging light, are a function of the ϕ dihedral angle of torsion about the central C C bond, assumed to lie in the y direction of the coordinate system.

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Computational study of basis set and electron correlation effects on anapole magnetizabilities of chiral molecules

Cited by 18 publications

References 38 publications

Physical achirality in geometrically chiral rotamers of hydrazine and boranylborane molecules

Physical achirality in geometrically chiral rotamers of hydrazine and boranylborane molecules

n the Validity of Minimum Magnetizability Principle in Chemical Reactions

On the axial chirality of leucoindigo

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