Origin-Independent Dynamic Polarizability Density from Coupled Cluster Response Theory.

The calculation of the origin-independent density of the dynamic electric dipole polarizability, previously presented for uncorrelated and density functional theory (DFT)-based methods, has been developed and implemented at the coupled cluster singles and doubles (CCSD) level of theory. A pointwise analysis of polarizability densities calculated for a number of molecules at Hartree-Fock (HF) and CCSD clearly shows that the electron correlation effect is much larger than one would argue considering the integrated dipole electric polarizability alone. Large error compensations occur during the integration process, which hide fairly large deviations mainly located in the internuclear regions. The same is observed when calculated CCSD and B3LYP polarizability densities are compared, with the remarkable feature that positive/negative deviations between CCSD and HF reverse sign, becoming negative/positive when comparing CCSD to B3LYP.

On the axial chirality of leucoindigo.

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. They vanish for symmetry reasons at ϕ = 0 ∘ and ϕ = 180 ∘ , corresponding respectively to C 2 v and C 2 h point group symmetries, that is, cis and trans conformers characterized by the presence of molecular symmetry planes. Nonetheless, diagonal components and average value of static anapole polarizability and optical rotation tensors vanish at ϕ = 90 ∘ , where leucondigo is unquestionably chiral from the geometrical viewpoint. Vanishing values of the average chiroptical properties have been observed also in the proximity of other ϕ angles. Attempts have been made to explain the occurrence of accidental zeros of chiroptical properties in terms of transition frequencies and scalar products appearing in the numerator of their quantum mechanical definitions. Within the electric dipole approximation, the presence of anomalous vanishing values of tensor components of anapole magnetizability and electric-magnetic dipole polarizability is ascribed to physical achirality, arising from the lack of either toroidal or spiral electron flow along the x , y and z directions.

Correction: Anisotropy of the vorticity tensor as a magnetic indicator of aromaticity.

Correction for 'Anisotropy of the vorticity tensor as a magnetic indicator of aromaticity' by S. Pelloni et al., Phys. Chem. Chem. Phys., 2020, 22, 1299-1305, DOI: .

Anisotropy of the vorticity tensor as a magnetic indicator of aromaticity.

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. The vorticity tensor is the nonsymmetric second-rank tensor obtained by differentiating the vorticity vector with respect to the components of B, i.e., . It is shown that isosurfaces of its anisotropy can be used as magnetotropicity indicators to detect electron delocalization effects and estimate the degree of aromaticity of cyclic molecules on the magnetic criterion.

Could Electronic Anapolar Interactions Drive Enantioselective Syntheses in Strongly Nonuniform Magnetic Fields? A Computational Study.

It is shown that the anapolar interaction of the electrons of a molecule with an external uniform magnetic field B and a uniform curl C = ∇ × B' determines different thermodynamic stabilization of the ground state for the enantiomers and diastereoisomers of a chiral molecule. A series of potential candidates for enantioselective syntheses have been investigated in a computational study via SCF-HF, B3LYP, and various coupled cluster approaches to determine the difference in energy between different enantiomers and diastereoisomers. The calculations show that these differences are very small for B and C presently available but approximately 3 orders of magnitude larger than those determined by parity violation effects. The chances that enantioselective synthesis may be attempted in the future are discussed. Recognition of anapolar interaction in chiral molecules via measurements of an induced magnetic dipole moment in the ordered phase may become possible in the presence of a nonuniform magnetic field with a strong gradient.

Electric Dipole-Magnetic Dipole Polarizability and Anapole Magnetizability of Hydrogen Peroxide as Functions of the HOOH Dihedral Angle.

The trace of tensors that account for chiroptical response of the H2O2 molecule is a function of the HO-OH dihedral angle. It vanishes at 0° and 180°, due to the presence of molecular symmetry planes, but also for values in the range 90-100° of this angle, in which the molecule is unquestionably chiral. Such an atypical effect is caused by counterbalancing contributions of diagonal tensor components with nearly maximal magnitude but opposite sign, determined by electron flow in open or closed helical paths, and associated with induced electric and magnetic dipole moments and anapole moments. For values of dihedral angle external to the 90-100° interval, the helical paths become smaller in size, thus reducing the amount of cancellation among diagonal components. Shrinking of helical paths determines the appearance of extremum values of tensor traces approximately at 50° and 140° dihedral angles.

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

Calculations have been carried out for C4H4X2 cyclic molecules, with X=O, S, Se, and Te, characterized by the presence of magnetic-field induced toroidal electron currents and associated orbital anapole moments. The orbital anapole induced by a static nonuniform magnetic field B, with uniform curl C=∇×B, is rationalized via a second-rank anapole magnetizability tensor a(αß), defined as minus the second derivative of the second-order interaction energy with respect to the components C(α) and B(ß). The average anapole magnetizability a̅ equals -χ̅, the pseudoscalar obtained by spatial averaging of the dipole-quadrupole magnetizability χ(α,ßγ). It has different sign for D and L enantiomeric systems and can therefore be used for chiral discrimination. Therefore, in an isotropic chiral medium, a homogeneous magnetic field induces an electronic anapole A(α), having the same magnitude, but opposite sign, for two enantiomorphs.

Magnetizabilities of diatomic and linear triatomic molecules in a time-independent nonuniform magnetic field.

The theory of response of a molecule in the presence of a static nonuniform magnetic field with uniform gradient is reviewed and extended. Induced magnetic dipole, quadrupole, and anapole moments are expressed via multipole magnetic susceptibilities. Dependence of response properties on the origin of the coordinate system with respect to which they are defined is investigated. Relationships describing the change of multipole and anapole susceptibilities in a translation of the reference system are reported. For a single molecule, two quantities are invariant and, in principle, experimentally measurable, that is, the induced magnetic dipole and the interaction energy. The trace of a second-rank anapole susceptibility, related to a pseudoscalar obtained by spatial averaging of the dipole-quadrupole susceptibility, of different sign for D and L enantiomeric systems, is origin independent. Therefore, in an isotropic chiral medium a homogeneous magnetic field induces an electronic anapole, having the same magnitude but opposite sign for two enantiomorphs. Calculations have been carried out for a set of diatomic and linear triatomic systems characterized by the presence of magnetic-field induced toroidal electron currents.

Assessment of the CTOCD-DZ method in a hierarchy of coupled cluster methods.

Gauge origin independent calculations of nuclear magnetic shielding tensors are carried out inside the formalism of the continuous transformation of the origin of the current density leading to formal annihilation of its diamagnetic contribution (CTOCD-DZ). We employ the unrelaxed linear response approach with a hierarchy of different coupled cluster methods in order to assess the importance of the level of approximation in the coupled cluster expansion. The basis set dependence of the computed nuclear magnetic shielding constants is also analyzed in the series of correlation consistent basis sets, with the aim of designing optimized basis sets of relatively small size.

Can Induced Orbital Paramagnetism Be Controlled by Strong Magnetic Fields?

Magnetic hypersusceptibilities and hypershielding at the nuclei of BH, CH(+), C4H4, and C8H8 molecules in the presence of an external spatially uniform, time-independent magnetic field have been investigated accounting for cubic response contributions via Rayleigh-Schrödinger perturbation theory. Numerical estimates have been obtained at the coupled Hartree-Fock and density-functional levels of theory within the conventional common-origin approach, using extended gaugeless basis sets. The fundamental role of electron correlation effects was assessed. Critical values of the applied magnetic field at which transition from paramagnetic to diamagnetic behavior would occur were estimated. It is shown that perturbative methods may successfully be employed to estimate the interaction energy for big cyclic molecules.

Electric quadrupole polarizabilities of nuclear magnetic shielding in some small molecules.

Computational procedures, based on (i) the Ramsey common origin approach and (ii) the continuous transformation of the origin of the quantum mechanical current density-diamagnetic zero (CTOCD-DZ), were applied at the Hartree-Fock level to determine electric quadrupole polarizabilities of nuclear magnetic shielding for molecules in the presence of a nonuniform electric field with a uniform gradient. The quadrupole polarizabilities depend on the origin of the coordinate system, but values of the magnetic field induced at a reference nucleus, determined via the CTOCD-DZ approach, are origin independent for any calculations relying on the algebraic approximation, irrespective of size and quality of the (gaugeless) basis set employed. On the other hand, theoretical estimates of the induced magnetic field obtained by single-origin methods are translationally invariant only in the limit of complete basis sets. Calculations of electric quadrupole polarizabilities of nuclear magnetic shielding are reported for H(2), HF, H(2)O, NH(3), and CH(4) molecules.

Chiral discrimination via nuclear magnetic shielding polarisabilities from NMR spectroscopy: theoretical study of (R(a))-1,3-dimethylallene, (2R)-2-methyloxirane, and (2R)-N-methyloxaziridine.

Three medium-size optically active molecules have been studied to make a guess at candidates suitable for chiral discrimination in an isotropic medium via nuclear magnetic resonance spectroscopy. The criterion for experimental detection is given by the magnitude of the isotropic part of nuclear magnetic shielding polarisability tensors, related to a pseudoscalar of opposite sign for the two enantiomers. The pseudoscalar shielding polarisability at the (17)O nucleus in N-methyloxaziridine, calculated at the Hartree-Fock level, is approximately 7.8 x10(-)(17) mV(-)(1). To obtain an experimentally observable magnetic field induced at the (17)O nucleus in N-methyloxaziridine, electric fields as large as approximately 10(7) - 10(8) Vm(-)(1) should be applied to the probe. The molecular electric dipole moment induced by precession of the magnetic dipole of the (17)O nucleus in a magnetic field of 10 T is, in absolute value, approximately 8.8 x 10(-)(42) Cm. The estimated rf-voltage at a resonance circuit is approximately 10 nV. Smaller values have been estimated for N, C, and H nuclei in 1,3-dimethylallene and 2-methyloxirane.

Calculation of the electric hypershielding at the nuclei of molecules in a strong magnetic field.

The third-rank electric hypershielding at the nuclei of 14 small molecules has been evaluated at the Hartree-Fock level of accuracy, by a pointwise procedure for the geometrical derivatives of magnetic susceptibilities and by a straightforward use of its definition within the Rayleigh-Schrodinger perturbation theory. The connection between these two quantities is provided by the Hellmann-Feynman theorem. The magnetically induced hypershielding at the nuclei accounts for distortion of molecular geometry caused by strong magnetic fields and for related changes of magnetic susceptibility. In homonuclear diatomics H(2), N(2), and F(2), a field along the bond direction squeezes the electron cloud toward the center, determining shorter but stronger bond. It is shown that constraints for rotational and translational invariances and hypervirial theorems provide a natural criterion for Hartree-Fock quality of computed nuclear electric hypershielding.

Diatropicity of tetraazanaphthalenes.

Tetraazanaphthalenes are diatropic molecules, whose magnetic response to a magnetic field perpendicular to the molecular plane closely resembles that of naphthalene. The out-of-plane component of the magnetic susceptibility tensor and its strong anisotropy can be used as quantifiers of magnetic aromaticity. Maps showing streamlines and modulus of the current density field provide clear evidence for diatropicity of these systems. They also explain the strong anisotropy of carbon and nitrogen magnetic shielding, which is determined by the big out-of-plane component of the nuclear shielding tensor. The electronic ring currents observed in the map deshield the nuclei of ring hydrogens by enforcing the local magnetic field and diminishing the out-of-plane component of proton shielding.

Why downfield proton chemical shifts are not reliable aromaticity indicators.

Traces of magnetizability, traces of magnetic shielding at the hydrogen nuclei, and nucleus-independent chemical shift are not reliable aromaticity quantifiers for planar conjugated hydrocarbons. A measure of aromaticity is provided by the out-of-plane tensor components, whose magnitude is influenced by the pi-ring currents. The failure of nucleus-independent chemical shift in this regard was proved for the molecule shown in the abstract graphic, sustaining a diatropic pi-current. The validity of the ring-current model is reaffirmed. [structure: see text]

Nonlinear response of the benzene molecule to strong magnetic fields.

The fourth-rank hypermagnetizability tensor of the benzene molecule has been evaluated at the coupled Hartree-Fock level of accuracy within the conventional common-origin approach, adopting gaugeless basis sets of increasing size and flexibility. The degree of convergence of theoretical tensor components has been estimated allowing for two different coordinate systems. It is shown that a strong magnetic field perpendicular to the plane of the molecule causes a distortion of the electron charge density, which tends to concentrate in the region of the C-C bonds. This charge contraction has a dynamical origin, and can be interpreted as a feedback effect in terms of the classical Lorentz force acting on the electron current density.

Ring current effects on nuclear magnetic shielding of carbon in the benzene molecule.

The differential Biot-Savart law of classical electrodynamics was applied to develop a ring current model for the magnetic shielding of the carbon nucleus in benzene. It is shown that the local effect of the pi currents, induced by a magnetic field normal to the molecular plane, on the sigmaC out-of-plane shielding tensor component vanishes. However, approximately 10% of sigmaC is due to the shielding contributions from pi current density in the region of the other carbon atoms. Magnetic shielding density maps obtained via quantum mechanical procedures confirm the predictions of the classical model.

Ring-current models from the differential Biot-Savart law.

The differential Biot-Savart law provides simple models for the pi ring currents induced in diatropic and paratropic planar conjugated molecules by a perpendicular magnetic field. The model predictions are confirmed by ab initio maps of nuclear magnetic shielding density. The effects on the protons and on the ring carbon atoms from the closest and furthest segments of the current loop are easily interpreted. [structure: see text]

Current density maps, magnetizability, and nuclear magnetic shielding tensors of bis-heteropentalenes. II. Furo-furan isomers.

Magnetic susceptibility and nuclear magnetic shielding at the nuclei of bis-heteropentalenes formed by two furan units ([2,3-b], [3,2-b], [3,4-b], and [3,4-c] isomers) have been computed by several approximated techniques and a large Gaussian basis set to achieve near Hartree-Fock estimates. Ab initio models of the ring currents induced by a magnetic field normal to the molecular plane were obtained for the three isomeric systems of higher symmetry, showing that the pi electrons give rise to intense diamagnetic circulation. The pi currents are responsible for enhanced magnetic anisotropy and strong out-of-plane proton deshielding. The theoretical findings are used to build up a "diatropicity matrix" for two fused five-membered heterocyclic systems.