On the computation of frequency-dependent molecular magnetizabilities via dynamical charge and current electron densities.

In the computation of molecular dynamic magnetizabilities and magnetic dipole moments, three different reference points are required: (i) origin of coordinate system, (ii) origin of vector potential A , and (iii) origin of multipole expansion. This study shows that methods relying on continuous translation of origin of the current density I B r ω t induced by optical magnetic fields provide an effective solution to the problem of choices (i) and (ii), in that they yield origin independent I B within the algebraic approximation, for any basis set. Frequency-dependent magnetizabilities are also invariant with respect to (iii), as a consequence of symmetry, for a number of molecular point groups. In molecules of lower symmetries, computed magnetizabilities depend on origin of the multipole expansion. Large basis set computations carried out for water, ammonia, methane, ethane, ethylene, boranylborane, and hydroxilamine, at the DFT level, have been reported to document these statements. A comparison is made for results obtained within the conventional common origin approach for static magnetic field. Sum rules for invariance of computed properties are discussed. Representations of streamlines and stagnation graphs of dynamical current density vector field induced in the water molecule by monochromatic waves of four frequencies are displayed.

Origin independent current density vector fields induced by time-dependent magnetic field. I. The LiH molecule.

The electronic current density, induced in a molecule by the optical magnetic field associated with a frequency-dependent monochromatic plane wave, assumed to be spatially uniform within the electric quadrupole approximation, has been studied by using a theoretical method based on a continuous translation of its origin. The induced electronic current density vector field designated by this procedure, invariant of the origin for any point of the molecular domain, is obtained via a computational scheme, formally annihilating the diamagnetic contribution of the conventional common-origin approach based on perturbation theory. In a preliminary application of the theoretical methods outlined in the present work, the simple molecule of lithium hydride has been investigated. Particular attention has been paid to the structure of induced electronic current density for several values of the magnetic field frequency by investigating equilibrium points of four different types, organized in stagnation lines, which constitute its stagnation graph, i.e., a topological fingerprint of the vector field conveying complete information in the condensed form, to verify the fulfillment of fundamental requirements, e.g., the continuity equation and the Poincaré-Hopf theorem on spherical and toroidal surfaces.

Dynamic toroidizability as ubiquitous property of atoms and molecules in optical electric fields.

The continuous search for metamaterials with special properties, suitable for new technological applications, is presently being driven by a preceding theoretical development, which took place after the introduction of new physical entities, anapole and a family of toroidal multipoles, having a border in common with those considered in the more familiar electric and magnetic multipole expansions. The related concept of toroidization, i.e., toroidal moment per unit volume, has been advocated in analogy to electric polarization and magnetization operated by electromagnetic fields and should be considered on the same footing regarding its relevance and practicality for understanding certain properties, e.g., ferrotoroidicity in condensed matter physics, and for rationalizing the behavior of charge-current distributions that neither radiate nor interact with external fields in classical and quantum electrodynamics. Toroidizability, i.e., the ability of sustaining toroidal moments, can also be defined by an analogy with electric polarizability and magnetizability. The present study shows that such a property is general and characterizes atoms and molecules and that the optical electric field of a light beam induces an oscillating anapole moment, i.e., the superposition of toroidal moment with an electric dipole moment. However, values of anapole polarizabilities induced by monochromatic light, estimated by time-dependent perturbation theory for rare gas atoms and a few molecules, are quite small and possibly hard to detect experimentally.

Electronic Currents Induced by Optical Fields and Rotatory Power Density in Chiral Molecules.

The electric dipole-magnetic dipole polarizability tensor κ', introduced to interpret the optical activity of chiral molecules, has been expressed in terms of a series of density functions kαß', which can be integrated all over the three-dimensional space to evaluate components καß' and trace καα'. A computational approach to kαß', based on frequency-dependent electronic current densities induced by monochromatic light shining on a probe molecule, has been developed. The dependence of kαß' on the origin of the coordinate system has been investigated in connection with the corresponding change of καß'. It is shown that only the trace kαα' of the density function defined via dynamic current density evaluated using the continuous translation of the origin of the coordinate system is invariant of the origin. Accordingly, this function is recommended as a tool that is quite useful for determining the molecular domains that determine optical activity to a major extent. A series of computations on the hydrogen peroxide molecule, for a number of different HO-OH dihedral angles, is shown to provide a pictorial documentation of the proposed method.

Synergistic Properties of Arabinogalactan (AG) and Hyaluronic Acid (HA) Sodium Salt Mixtures.

The properties of mixtures of two polysaccharides, arabinogalactan (AG) and hyaluronic acid (HA), were investigated in solution by the measurement of diffusion coefficients D of water protons by DOSY (Diffusion Ordered SpectroscopY), by the determination of viscosity and by the investigation of the affinity of a small molecule molecular probe versus AG/HA mixtures in the presence of bovine submaxillary mucin (BSM) by 1HNMR spectroscopy. Enhanced mucoadhesive properties, decreased mobility of water and decreased viscosity were observed at the increase of AG/HA ratio and of total concentration of AG. This unusual combination of properties can lead to more effective and long-lasting hydration of certain tissues (inflamed skin, dry eye corneal surface, etc.) and can be useful in the preparation of new formulations of cosmetics and of drug release systems, with the advantage of reducing the viscosity of the solutions.

Spin Currents Induced in Open-Shell Molecules by Static and Uniform Magnetic and Electric Fields in the Presence of a Spin-Orbit Coupling Interaction and Conservation Law.

The derivation of the total induced current density vector field, in the presence of static and uniform magnetic and electric fields, is illustrated in a more clear and formally correct language together with a discussion on the charge-current conservation law not presented before for the spin-orbit coupling contribution. The theory here exposed turns out to be in fully agreement with the theory of Special Relativity and it is applicable to open-shell molecules in the presence of a nonvanishing spin orbit coupling. The discussion here exposed turns out to be accurately valid for a strictly central field due to the chosen approximation of the spin-orbit coupling Hamiltonian, but it is appropriate to deal correctly with molecular systems. The ab initio calculation of spin current densities has been implemented at both unrestricted Hartree-Fock and unrestricted DFT levels of theory. Some maps of spin currents on molecules of interest, i.e., the CH3 radical and the superoctazethrene molecule are also illustrated.

Origin-Independent Densities of Static and Dynamic Molecular Polarizabilities.

The notion of the electric dipole polarizability density function of atoms and molecules has been considered. The current density induced by the time derivative of the electric field of monochromatic light allows for a new definition of the electric dipole polarizability density, which is translationally invariant. This translational invariance provides the physical meaning that was lacking in previous defined polarizability densities. The new polarizability density has been implemented at the TD-DFT level of theory. The origin independence has been proven in silico to hold regardless of the basis set size. Two emblematic molecules, i.e., CO and N2, which in many respects display similar electric response, have been studied in detail. The substantial differences, which have been highlighted in the topology of the parallel and perpendicular polarizability density tensor components of CO and N2, are grossly hidden by compensation, when integration is carried out to get the molecular properties.