Theoretical estimates of the anapole magnetizabilities of C4H4X2 cyclic molecules for X=O, S, Se, and Te

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

doi:10.1063/1.4893991

Cited by 16 publications

(48 citation statements)

References 69 publications

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“…The anapole magnetizabilities are second‐rank tensors, defined by derivatives of the second‐order RSPT energy or derivatives of the induced anapole and dipole moments, see the introductory section. They are expressed as sums of paramagnetic and diamagnetic contributions,

a_{α β} = a_{α β}^{normalp} + a_{α β}^{normald},

b_{α β} = b_{α β}^{normalp} + b_{α β}^{normald},

specified via the formulae

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

a_{α β}^{normald} = \frac{e^{2}}{12 m_{normale}} ɛ_{α β γ} 〈 a | \sum_{i = 1}^{n} {(r^{2} r_{γ})}_{i} | a 〉,

b_{α β}^{normalp} = \frac{1}{ℏ} \sum_{j \neq a} \frac{2}{ω_{j a}} ℜ (〈 a | {\overset{a}{true}}_{α} | j 〉 〈 j | {\overset{a}{true}}_{β} | a 〉),

b_{α β}^{normald} = - e

…”

Section: Anapole Moment and Anapole Magnetizabilitiesmentioning

confidence: 99%

“…Within standard tensor notation, for example, allowing for the Einstein convention of implicit summation over repeated Greek indices, the anapole magnetizability is defined by contracting the mixed dipole/quadrupole magnetizability with the Levi–Civita third‐rank pseudotensor,

a_{α β} = - (1 / 2) ɛ_{α λ μ} χ_{β, λ μ}

. It can be rewritten as a second derivative of the energy W BC , and as the first derivative of either the induced anapole

scriptA

or magnetic dipole

bold-italicM

with respect to the components of

bold-italicB

and

C = \nabla \times B

a_{α β} = - \frac{\partial^{2} W^{B C}}{\partial C_{α} \partial B_{β}} = \frac{\partial {scriptA}_{α}}{\partial B_{β}} = \frac{\partial M_{β}}{\partial C_{α}} .

…”

Section: Introductionmentioning

confidence: 99%

“…It is a parity‐odd, time‐even second‐rank tensor. Therefore, the anapolar contribution

W^{B C} = - a_{α β} C_{α} B_{β}

to the interaction energy has the same magnitude, but opposite sign, for two enantiomeric molecules . A nonperturbative approach based on these definitions has been recently applied to evaluate the relevant tensors, employing a powerful computational scheme previously developed to investigate linear and nonlinear atomic and molecular response to strong magnetic fields via basis sets of London orbitals .…”

Section: Introductionmentioning

confidence: 99%

“…Previous calculations allowing for SCF approaches have shown that the magnetizabilities χ α , βγ and a αβ are characterized by very small magnitude, which suggests that their experimental determination may be quite difficult. Whereas electron correlation contributions to the second rank magnetizability χ αβ are known to be relatively small in general, somewhat larger correlation contributions seem to affect third‐rank magnetic dipole/magnetic quadrupole magnetizabilities and related anapole magnetizability of C 4 H 4 X 2 cyclic molecules for X = O, S, Se, and Te, which is expected on inspection of their definitions, eqs. and , involving an additional power of the position operator …”

Section: Introductionmentioning

confidence: 99%

“…The present article sets out to provide further indications in this direction. It is also aimed at (i) reshaping the definition of anapole magnetizabilities in a simpler and more compact form within the RSPT scheme in view of computational applications, (ii) defining diamagnetic and paramagnetic contributions to the electronic current density vector induced by the curl

bold-italicC

, in terms of which alternative expressions of the interaction energy are written, (iii) applying the theory to evaluate a αβ anapole magnetizabilities in a series of chiral molecules to investigate the role of basis set quality and the effects of electron correlation on the pseudoscalar a αα , characterized by the same magnitude but opposite sign for enantiomeric compounds. Results are reported in Calculations of anapole magnetizabilities for chiral molecules in a magnetic field with uniform curl section.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2016

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In the presence of a static, nonhomogeneous magnetic field, represented by the axial vector B at the origin of the coordinate system and by the polar vector C=∇×B, assumed to be spatially uniform, the chiral molecules investigated in this paper carry an orbital electronic anapole, described by the polar vector A. The electronic interaction energy of these molecules in nonordered media is a cross term, coupling B and C via a¯, one third of the trace of the anapole magnetizability aαβ tensor, that is, WBC=-a¯B·C. Both A and W(BC) have opposite sign in the two enantiomeric forms, a fact quite remarkable from the conceptual point of view. The magnitude of a¯ predicted in the present computational investigation for five chiral molecules is very small and significantly biased by electron correlation contributions, estimated at the density functional level via three different functionals. © 2016 Wiley Periodicals, Inc.

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a_{α β} = a_{α β}^{normalp} + a_{α β}^{normald},

b_{α β} = b_{α β}^{normalp} + b_{α β}^{normald},

specified via the formulae

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

a_{α β}^{normald} = \frac{e^{2}}{12 m_{normale}} ɛ_{α β γ} 〈 a | \sum_{i = 1}^{n} {(r^{2} r_{γ})}_{i} | a 〉,

b_{α β}^{normalp} = \frac{1}{ℏ} \sum_{j \neq a} \frac{2}{ω_{j a}} ℜ (〈 a | {\overset{a}{true}}_{α} | j 〉 〈 j | {\overset{a}{true}}_{β} | a 〉),

b_{α β}^{normald} = - e

…”

Section: Anapole Moment and Anapole Magnetizabilitiesmentioning

confidence: 99%

a_{α β} = - (1 / 2) ɛ_{α λ μ} χ_{β, λ μ}

. It can be rewritten as a second derivative of the energy W BC , and as the first derivative of either the induced anapole

scriptA

or magnetic dipole

bold-italicM

with respect to the components of

bold-italicB

and

C = \nabla \times B

a_{α β} = - \frac{\partial^{2} W^{B C}}{\partial C_{α} \partial B_{β}} = \frac{\partial {scriptA}_{α}}{\partial B_{β}} = \frac{\partial M_{β}}{\partial C_{α}} .

…”

Section: Introductionmentioning

confidence: 99%

“…It is a parity‐odd, time‐even second‐rank tensor. Therefore, the anapolar contribution

W^{B C} = - a_{α β} C_{α} B_{β}

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

bold-italicC

Section: Introductionmentioning

confidence: 99%

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

et al. 2016

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Calculations of magnetically induced current densities: theory and applications

Sundholm

Fliegl

Berger

2016

WIREs Comput Mol Sci

309

543

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A review of computational studies of magnetically induced current density susceptibilities in molecules and their relation to experiments is presented. The history of the investigation of magnetically induced current densities and ring currents in molecules is briefly covered. The theoretical development of relativistic and nonrelativistic computational approaches for computing current densities in closed-shell and open-shell molecules is discussed and different state of the art methods to interpret calculated current densities are reviewed. Numerical integration approaches to assess global, semilocal, and local aromatic properties of multiring molecules are presented and demonstrated on free-base trans-porphyrin. We show that numerical integration of the current density combined with guiding visualization techniques of the current flow is a powerful tool for studies of the aromatic character of complicated molecular structures such as annelated aromatic and antiaromatic rings. Representative applications are reported illustrating the importance of careful current density studies for organic and inorganic chemistry. The applications include calculations of current densities and current strengths for aromatic, antiaromatic, and nonaromatic molecules of different kind. Current densities in spherical, cylindrical, tetrahedral, toroidal, and Möbius-twisted molecules are discussed. The aromatic character, current pathways, and current strengths of porphyrins are briefly highlighted. Aromatic properties of inorganic molecules are assessed based on current density calculations. Current strengths as a noninvasive tool to determine strengths of hydrogen bonds are discussed.

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Topology of Quantum Mechanical Current Density Vector Fields Induced in a Molecule by Static Magnetic Perturbations

Lazzeretti

2016

Challenges and Advances in Computational Chemistry and Physics

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Theoretical estimates of the anapole magnetizabilities of C4H4X2 cyclic molecules for X=O, S, Se, and Te

Cited by 16 publications

References 69 publications

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

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

Calculations of magnetically induced current densities: theory and applications

Topology of Quantum Mechanical Current Density Vector Fields Induced in a Molecule by Static Magnetic Perturbations

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