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Paolo Lazzeretti - One of the best experts on this subject based on the ideXlab platform.
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computational study of basis set and electron correlation effects on anapole magnetizabilities of chiral molecules
Journal of Computational Chemistry, 2016Co-Authors: Natalia Zarycz, Stefano Pelloni, Patricio F Provasi, G I Pagola, Marta B Ferraro, Paolo LazzerettiAbstract:: 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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on the definition of molecular dynamic Magnetizability
Theoretical Chemistry Accounts, 2015Co-Authors: Paolo LazzerettiAbstract:The possibility of defining a second-rank tensor $$\xi _{\alpha \beta,} $$ which would account for the frequency-dependent Magnetizability of a molecule in the presence of an optical field, represented as a monochromatic wave, has been investigated. It has been shown that, whereas the electric dipole moment induced by the incident wave is origin independent, the magnetic dipole depends on the origin and cannot be rationalized via a function $$M_{\alpha }=\xi _{\alpha \beta }B_{\beta }$$ of the magnetic field $$B_{\beta }$$ . This result was arrived at using time-dependent perturbation theory, within dipole, quadrupole, and octopole approximations for the interaction Hamiltonian, employing a series of relationships, which describe the change of molecular response tensors in a change of origin of the coordinate system.
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Polygonal current model: an effective quantifier of aromaticity on the magnetic criterion.
The journal of physical chemistry. A, 2013Co-Authors: Stefano Pelloni, Paolo LazzerettiAbstract:To explain peculiar effects of electron delocalization on the magnetic response of planar cyclic molecules, a basic model that accounts for their actual geometrical structure has been developed by integrating the differential Biot–Savart law. Such a model, based on a single polygonal circuit with ideal features, is shown to be applicable to electrically neutral or charged monocyclic compounds, as well as linear polycyclic condensed hydrocarbons. Two theoretical quantities, easily computed via quantum chemistry codes (the out-of-plane components of the Magnetizability, ξ∥, and the magnetic shielding σ∥(h) of points P on the symmetry axis orthogonal to the molecular plane, at distance h from the center of mass) are shown to be linearly connected, for example, for monocyclic structures, via the relationship σ∥(h) = ±(μ0/2π)ξ∥D(h), where D(h) is a simple function of geometrical parameters. Equations of this type are useful to rationalize scan profiles of magnetic shielding and nucleus-independent chemical shi...
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correlation between the out of plane components of Magnetizability and central magnetic shielding in unsaturated cyclic molecules
Journal of Physical Chemistry A, 2011Co-Authors: Stefano Pelloni, Paolo LazzerettiAbstract:A simple classical model of magnetic-field induced π-electron flow is discussed, showing that the contribution to the σ∥ out-of-plane component of the virtual magnetic shielding provided by π-ring currents, at points P along the Cn axis of cyclic planar unsaturated hydrocarbons CnHn with Dnh symmetry, in the presence of a magnetic field Bext at right angles to the σh plane, is, with good approximation, connected with the π-electron contribution to the out-of-plane component of the Magnetizability, ξ∥. The relationship is σ∥(h) = −(μ0/2π)(s2 + h2)−3/2ξ∥, where s is the distance of a C nucleus from the center of the carbon ring, and h is the distance of P from σh. The ring current susceptibility, that is, the strength of the π currents, expressed in nA/T (nano ampere per tesla) within the SI system of units, is given by ∂I/∂Bext = −ξ∥/(πs2), which can be used as a reliable virtual measure of magnetotropicity and relative π-electron mobility in isoelectronic systems. Criteria for the practicality of the prop...
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Beyond NICS: estimation of the magnetotropicity of inorganic unsaturated planar rings
'Royal Society of Chemistry (RSC)', 2011Co-Authors: Stefano Pelloni, Guglielmo Monaco, Paolo Lazzeretti, Riccardo ZanasiAbstract:A simple classical model of magnetic-field induced electron flow is used to evaluate the ring current strength for a few inorganic monocyclic compounds. It is shown that, for these neutral and charged systems, sustaining delocalized electron currents in the presence of a magnetic field Bext orthogonal to the sh plane, the out-of-plane component of the nuclear magnetic shielding along the central axis is connected to the out-of-plane Magnetizability by a simple equation, involving the radius of an average loop of current. A novel estimate of this effective radius is provided. Reliable ring current susceptibilities (that is, current strengths) can be evaluated by a simple relationship, using the out-of-plane components of nuclear shielding and Magnetizability tensors. The accuracy of the current susceptibilities calculated by the classical model is established by comparison with corresponding ab initio estimates obtained by integrating the quantum mechanical current-density vector field. The out-of-plane components of nuclear shielding and Magnetizability are both strongly biased by the molecular geometry. Their combined use to estimate the ring current susceptibility offers a quantifier of magnetotropicity more reliable than (i) the out-of-plane component of Magnetizability, (ii) the out-of-plane component of the magnetic shielding at the center of mass. The inadequacy of these commonly adopted magnetotropicity measures is demonstrated by comparing a set of related molecules, C6H6 and Si6H6, N6 and P6
Trygve Helgaker - One of the best experts on this subject based on the ideXlab platform.
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Magnetizabilities and Nuclear Shielding Constants of the Fluoromethanes in the Gas Phase and Solution
2016Co-Authors: Per-olof A Str, Kenneth Ruud, Kurt V. Mikkelsen, Trygve HelgakerAbstract:The effects of a dielectric medium on the magnetizabilities and nuclear shielding constants of the fluoromethanes are calculated in a gauge-origin independent approach. It is shown that in order to model the effects of a dielectric medium properly, we have to go beyond the dipole approximation and the geometry has to be optimized for each value of the dielectric constant. Geometrical distortions play an important role, as is clearly demonstrated for the Magnetizability of the CH3F molecule where the geometrical distortions alter the sign of the dielectric contribution to the solvent shift. The effects on the nuclear shielding constants from a dielectric medium are interpreted in terms of the polarization of the charge distribution and the change in geometry. Other medium effects on nuclear shielding constants are discussed, and it is demonstrated that they must be included in order to reproduce the experimental gas-to-liquid chemical shift of the CH3F and CHF3 molecules. Basis set convergence and electron correlation effects of the magnetizabilities and the nuclear shielding constants in the gas phase are also investigated. I
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the Magnetizability rotational g tensor and quadrupole moment of the boron trihalides
Molecular Physics, 2006Co-Authors: David J D Wilson, Trygve Helgaker, Antonio RizzoAbstract:We present the results of an ab initio study of the molecular Zeeman properties—that is, the magnetizabilities, rotational g tensors, and electric quadrupole moments—for BX3 (X = F, Cl, Br, I) within Hartree–Fock and density-functional theories. Basis-set convergence is ensured by the use of large basis sets of London atomic orbitals. Calculated trends are discussed and comparisons are made with available experimental data.
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density functional theory study of electric and magnetic properties of hexafluorobenzene in the vapor phase
Journal of Chemical Physics, 2005Co-Authors: Antonio Rizzo, Trygve Helgaker, Chiara Cappelli, Branislav Jansik, Dan Jonsson, Pawel Salek, Sonia Coriani, David J D Wilson, Hans AgrenAbstract:A series of electric and magnetic properties of hexafluorobenzene have been calculated, including the electric dipole polarizability, Magnetizability, electric quadrupole moment, and nonlinear mixed electric dipole-magnetic dipole-electric quadrupole hyperpolarizabilities needed to obtain estimates of the Kerr, Cotton-Mouton, Buckingham, Jones, and magnetoelectric birefringences in the vapor phase. Time-dependent density-functional theory was employed for the calculation of linear-, quadratic, and cubic response functions. A number of density functionals have been considered, along with Sadlej's triple-zeta basis set and the augmented correlation-consistent polarized valence double zeta and augmented correlation-consistent polarized valence triple zeta basis sets. Comparisons have been made with experiment where possible. The analysis of results allows for an assessment of the capability of time-dependent density-functional theory for high-order electromagnetic properties of an electron-rich system such as hexafluorobenzene.
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Density functional theory study of electric and magnetic properties of hexafluorobenzene in the vapor phase
'AIP Publishing', 2005Co-Authors: A. Rizzo, Trygve Helgaker, Branislav Jansik, Dan Jonsson, Sonia Coriani, Cappelli C, Sa P. Lek, D. J. D, Hans AgrenAbstract:A series of electric and magnetic properties of hexafluorobenzene have been calculated, including the electric dipole polarizability, Magnetizability, electric quadrupole moment, and nonlinear mixed electric dipole-magnetic dipole-electric quadrupole hyperpolarizabilities needed to obtain estimates of the Kerr, Cotton-Mouton, Buckingham, Jones, and magnetoelectric birefringences in the vapor phase. Time-dependent density-functional theory was employed for the calculation of linear-, quadratic, and cubic response functions. A number of density functionals have been considered, along with Sadlej’s triple-z basis set and the augmented correlation-consistent polarized valence double zeta and augmented correlation-consistent polarized valence triple zeta basis sets. Comparisons have been made with experiment where possible. The analysis of results allows for an assessment of the capability of time-dependent density-functional theory for high-order electromagnetic properties of an electron-rich system such as hexafluorobenzene
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rovibrationally averaged Magnetizability rotational g factor and indirect spin spin coupling of the hydrogen fluoride molecule
Journal of Chemical Physics, 1999Co-Authors: Perolof Astrand, Kenneth Ruud, Kurt V. Mikkelsen, Trygve HelgakerAbstract:The Magnetizability tensor, the rotational g factor, and the indirect nuclear spin–spin coupling constant of the hydrogen fluoride molecule have been calculated using large multiconfigurational self-consistent field wave functions and large basis sets. For a critical comparison with experiment, rovibrational corrections have also been calculated. For the Magnetizability tensor and the spin–spin coupling constant, we present results with higher precision than available experimental data; for the rotational g factor, our results are in good agreement with experiment.
Riccardo Zanasi - One of the best experts on this subject based on the ideXlab platform.
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Magnetically Induced Current Density Spatial Domains
2019Co-Authors: Guglielmo Monaco, Riccardo ZanasiAbstract:The pseudostagnation graphs of the current density induced by a magnetic field perpendicular to the plane of the carbon atoms of benzene and cyclopropane, chosen as archetypal of π- and σ-aromatic molecules, have been worked out. Saddle nodes forming the saddle stagnation lines of the pseudostagnation graph have been connected by means of trajectories of the current density, which delimit the border of four different sectors of flow around each saddle line. The merging of all such boundary trajectories provides local zero-flux surfaces in the pseudocurrent density, i.e., separatrices, which split the induced current density field in a number of three-dimensional domains of flow. As a result, a new partition scheme, corresponding to the physical flow that one could observe, has been obtained. For benzene and cyclopropane, by integration of the current density over the various spatial domains, the parallel component of the nuclear magnetic shielding and Magnetizability tensors has been decomposed into contributions that are hard to reconcile with any atomic models of partition
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AACID: Anisotropy of the Asymmetric Magnetically Induced Current Density Tensor
2018Co-Authors: Guglielmo Monaco, Riccardo ZanasiAbstract:Molecular magnetic properties, such as the Magnetizability, the magnetic shielding, and the current strength, all stem from the asymmetric current density tensor. The anisotropy of that tensor, previously defined from its symmetric component only, is a scalar field expected to bear useful information on molecular structure. A more general anisotropy has here been defined, considering the full asymmetric tensor and its eigenvalues in the complex plane. Computations on a few prototypical aromatic molecules show that the anisotropy of the full tensor highlights previously missed structural features and also changes in a more regular way with bond length, as compared to the already known anisotropy of the symmetric component of the tensor
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Beyond NICS
'AIP Publishing', 2012Co-Authors: Stefano Pelloni, Guglielmo Monaco, Riccardo Zanasi, And Paolo LazzerettiAbstract:A ring current model describing the flow of delocalized electrons, induced in unsaturated molecules by a magnetic field perpendicular to the molecular plane, has been developed to define simple and practical indices of current strength, which provide a reliable measure of aromaticity on the magnetic criterion. Comparison with corresponding ab initio estimates of current strength for a series of aromatic and antiaromatic systems is used to assess the quality of the proposed indices, which are shown to be preferable to others currently used, e.g., out-of-plane components of Magnetizability, ξ‖, and NICS‖. It is also shown that these quantities are both biased by spurious geometrical parameters, which limit their practicality. In particular, NICS‖ depends on the inverse of the ring radius and it does not provide acceptable magnetotropicity scales
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Beyond NICS
'AIP Publishing', 2012Co-Authors: Pelloni Stefano, Riccardo Zanasi, Guglielmo Monaco, Lazzeretti PaoloAbstract:A ring current model describing the flow of delocalized electrons, induced in unsaturated molecules by a magnetic field perpendicular to the molecular plane, has been developed to define simple and practical indices of current strength, which provide a reliable measure of aromaticity on the magnetic criterion. Comparison with corresponding ab initio estimates of current strength for a series of aromatic and antiaromatic systems is used to assess the quality of the proposed indices, which are shown to be preferable to others currently used, e.g., out-of-plane components of Magnetizability, xi(parallel to), and NICS parallel to. It is also shown that these quantities are both biased by spurious geometrical parameters, which limit their practicality. In particular, NICS parallel to depends on the inverse of the ring radius and it does not provide acceptable magnetotropicity scales
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Beyond NICS: estimation of the magnetotropicity of inorganic unsaturated planar rings
'Royal Society of Chemistry (RSC)', 2011Co-Authors: Stefano Pelloni, Guglielmo Monaco, Paolo Lazzeretti, Riccardo ZanasiAbstract:A simple classical model of magnetic-field induced electron flow is used to evaluate the ring current strength for a few inorganic monocyclic compounds. It is shown that, for these neutral and charged systems, sustaining delocalized electron currents in the presence of a magnetic field Bext orthogonal to the sh plane, the out-of-plane component of the nuclear magnetic shielding along the central axis is connected to the out-of-plane Magnetizability by a simple equation, involving the radius of an average loop of current. A novel estimate of this effective radius is provided. Reliable ring current susceptibilities (that is, current strengths) can be evaluated by a simple relationship, using the out-of-plane components of nuclear shielding and Magnetizability tensors. The accuracy of the current susceptibilities calculated by the classical model is established by comparison with corresponding ab initio estimates obtained by integrating the quantum mechanical current-density vector field. The out-of-plane components of nuclear shielding and Magnetizability are both strongly biased by the molecular geometry. Their combined use to estimate the ring current susceptibility offers a quantifier of magnetotropicity more reliable than (i) the out-of-plane component of Magnetizability, (ii) the out-of-plane component of the magnetic shielding at the center of mass. The inadequacy of these commonly adopted magnetotropicity measures is demonstrated by comparing a set of related molecules, C6H6 and Si6H6, N6 and P6
Stefano Pelloni - One of the best experts on this subject based on the ideXlab platform.
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computational study of basis set and electron correlation effects on anapole magnetizabilities of chiral molecules
Journal of Computational Chemistry, 2016Co-Authors: Natalia Zarycz, Stefano Pelloni, Patricio F Provasi, G I Pagola, Marta B Ferraro, Paolo LazzerettiAbstract:: 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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Polygonal current model: an effective quantifier of aromaticity on the magnetic criterion.
The journal of physical chemistry. A, 2013Co-Authors: Stefano Pelloni, Paolo LazzerettiAbstract:To explain peculiar effects of electron delocalization on the magnetic response of planar cyclic molecules, a basic model that accounts for their actual geometrical structure has been developed by integrating the differential Biot–Savart law. Such a model, based on a single polygonal circuit with ideal features, is shown to be applicable to electrically neutral or charged monocyclic compounds, as well as linear polycyclic condensed hydrocarbons. Two theoretical quantities, easily computed via quantum chemistry codes (the out-of-plane components of the Magnetizability, ξ∥, and the magnetic shielding σ∥(h) of points P on the symmetry axis orthogonal to the molecular plane, at distance h from the center of mass) are shown to be linearly connected, for example, for monocyclic structures, via the relationship σ∥(h) = ±(μ0/2π)ξ∥D(h), where D(h) is a simple function of geometrical parameters. Equations of this type are useful to rationalize scan profiles of magnetic shielding and nucleus-independent chemical shi...
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Beyond NICS
'AIP Publishing', 2012Co-Authors: Stefano Pelloni, Guglielmo Monaco, Riccardo Zanasi, And Paolo LazzerettiAbstract:A ring current model describing the flow of delocalized electrons, induced in unsaturated molecules by a magnetic field perpendicular to the molecular plane, has been developed to define simple and practical indices of current strength, which provide a reliable measure of aromaticity on the magnetic criterion. Comparison with corresponding ab initio estimates of current strength for a series of aromatic and antiaromatic systems is used to assess the quality of the proposed indices, which are shown to be preferable to others currently used, e.g., out-of-plane components of Magnetizability, ξ‖, and NICS‖. It is also shown that these quantities are both biased by spurious geometrical parameters, which limit their practicality. In particular, NICS‖ depends on the inverse of the ring radius and it does not provide acceptable magnetotropicity scales
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correlation between the out of plane components of Magnetizability and central magnetic shielding in unsaturated cyclic molecules
Journal of Physical Chemistry A, 2011Co-Authors: Stefano Pelloni, Paolo LazzerettiAbstract:A simple classical model of magnetic-field induced π-electron flow is discussed, showing that the contribution to the σ∥ out-of-plane component of the virtual magnetic shielding provided by π-ring currents, at points P along the Cn axis of cyclic planar unsaturated hydrocarbons CnHn with Dnh symmetry, in the presence of a magnetic field Bext at right angles to the σh plane, is, with good approximation, connected with the π-electron contribution to the out-of-plane component of the Magnetizability, ξ∥. The relationship is σ∥(h) = −(μ0/2π)(s2 + h2)−3/2ξ∥, where s is the distance of a C nucleus from the center of the carbon ring, and h is the distance of P from σh. The ring current susceptibility, that is, the strength of the π currents, expressed in nA/T (nano ampere per tesla) within the SI system of units, is given by ∂I/∂Bext = −ξ∥/(πs2), which can be used as a reliable virtual measure of magnetotropicity and relative π-electron mobility in isoelectronic systems. Criteria for the practicality of the prop...
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Beyond NICS: estimation of the magnetotropicity of inorganic unsaturated planar rings
'Royal Society of Chemistry (RSC)', 2011Co-Authors: Stefano Pelloni, Guglielmo Monaco, Paolo Lazzeretti, Riccardo ZanasiAbstract:A simple classical model of magnetic-field induced electron flow is used to evaluate the ring current strength for a few inorganic monocyclic compounds. It is shown that, for these neutral and charged systems, sustaining delocalized electron currents in the presence of a magnetic field Bext orthogonal to the sh plane, the out-of-plane component of the nuclear magnetic shielding along the central axis is connected to the out-of-plane Magnetizability by a simple equation, involving the radius of an average loop of current. A novel estimate of this effective radius is provided. Reliable ring current susceptibilities (that is, current strengths) can be evaluated by a simple relationship, using the out-of-plane components of nuclear shielding and Magnetizability tensors. The accuracy of the current susceptibilities calculated by the classical model is established by comparison with corresponding ab initio estimates obtained by integrating the quantum mechanical current-density vector field. The out-of-plane components of nuclear shielding and Magnetizability are both strongly biased by the molecular geometry. Their combined use to estimate the ring current susceptibility offers a quantifier of magnetotropicity more reliable than (i) the out-of-plane component of Magnetizability, (ii) the out-of-plane component of the magnetic shielding at the center of mass. The inadequacy of these commonly adopted magnetotropicity measures is demonstrated by comparing a set of related molecules, C6H6 and Si6H6, N6 and P6
Andreas M. Köster - One of the best experts on this subject based on the ideXlab platform.
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efficient calculation of the rotational g tensor from auxiliary density functional theory
Journal of Physical Chemistry A, 2015Co-Authors: Bernardo Zunigagutierrez, Monica Camachogonzalez, Patricia Simonbastida, Alfonso Bendanacastillo, Patrizia Calaminici, Andreas M. KösterAbstract:: The computation of the rotational g tensor with the recently developed auxiliary density functional theory (ADFT) gauge including atomic orbital (GIAO) methodology is presented. For the rotational g tensor, the calculation of the Magnetizability tensor represents the most demanding computational task. With the ADFT-GIAO methodology, the CPU time for the Magnetizability tensor calculation can be dramatically reduced. Therefore, it seems most desirable to employ the ADFT-GIAO methodology also for the computation of the rotational g tensor. In this work, the quality of rotational g tensors obtained with the ADFT-GIAO methodology is compared with available experimental data as well as with other theoretical results at the Hartree-Fock and coupled-cluster level of theory. It is found that the agreement between the ADFT-GIAO results and the experiment is good. Furthermore, we also show that the ADFT-GIAO g tensor calculation is applicable to large systems like carbon nanotube models containing hundreds of atom and thousands of basis functions.
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Magnetizability tensors from auxiliary density functional theory
Journal of Chemical Physics, 2012Co-Authors: Bernardo Zunigagutierrez, Gerald Geudtner, Andreas M. KösterAbstract:The working equations for the calculation of the Magnetizability tensor in the framework of auxiliary density functional theory with gauge including atomic orbitals (ADFT-GIAO) are derived. Unlike in the corresponding conventional density functional theory implementations the numerical integration of the GIAOs is avoided in ADFT-GIAO. Our validation shows that this simplification has no effect on the accuracy of the methodology. As a result, a reliable and efficient implementation for the calculation of magnetizabilities of systems with more than 1000 atoms and 14 000 basis functions is presented.