Frequency-dependent current density tensors as density functions of dynamic polarizabilities

Standard Response Calculation of Electric Dipole Polarizability and Specific Optical Rotation Power Densities

A time-dependent method has been developed to solve the standard response equation for the calculation of dynamic molecular property densities, endowed with the characteristic of being origin-invariant, entirely in the atomic orbital basis at both HF and DFT level of theory. The method has been tuned in particular for the calculation of origin-independent electric dipole polarizability density and specific rotation power density. Some demonstrations are given for the hexabenzocoronene molecule and the Tröger's base.

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.

Electronic current densities and origin-independent property densities induced by optical fields

The interaction of a molecule with optical fields is customarily interpreted by means of induced time-dependent electric polarizabilities, magnetizabilities and mixed electric-magnetic polarizabilities. In general, these properties can be rationalized by integrals of density functions formulated in terms of induced charge and current densities. In this perspective, we focus on what has been done so far at the theoretical level, and on what can be expected to be unveiled from the topological study of suitable density functions, endowed with the fundamental requirement of origin invariance. Densities characterized by such a property can be integrated all over the configuration space to obtain electric dipole polarizability and optical rotatory power. Corresponding maps visualize domains mainly involved in the molecular response. The diagonal components of origin-independent density tensor functions that, on integration, yield corresponding electric dipole polarizability tensor of benzene, naphthalene, phenanthrene and ovalene, have been computed, confirming the ubiquitous presence of counter-polarization regions in the proximity of the atomic nuclei. They are associated with toroidal electron currents, induced by time derivative of the electric field of impinging radiation. Electron (de)localization in these systems is readily observed and estimated. The optical rotation density of the carbonyl chromophore is studied in detail. Its essential feature is the separation in quadrants of alternating sign of density about the CO bond. The presence of an extrachromophoric perturbation determines asymmetry in the extension of the quadrant distribution, thus causing optical rotation.

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.

Electronic Currents and Anapolar Response Induced in Molecules by Monochromatic Light

It is shown that the electric dipole- and electric quadrupole–anapole polarizabilities, denoted respectively by fαβ′ and gα,βγ′, and the anapole magnetizability aαβ, are intrinsic properties of the electron cloud of molecules responding to optical fields. fαβ′ is a nonvanishing property of chiral and achiral compounds, whereas aαβ is suitable for enantiomer discrimination of chiral species. They can conveniently be evaluated by numerical integration, employing a formulation complementary to that provided by perturbation theory and relying on the preliminary computation of electronic current density tensors all over the molecular domain. The origin dependence of the dynamic anapolar response is rationalized via related computational techniques employing numerical integration, as well as definitions of molecular property tensors, for example, electric dipole and electric quadrupole polarizabilties and magnetizability. A preliminary application of the theory is reported for the Ra enantiomer of the hydrogen peroxide molecule, evaluating tensor components of electric dipole-anapole polarizability and anapole magnetizability as functions of the dihedral angle ϕ≡∠ H-O-O-H in the range 0∘≤ϕ≤180∘.

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 kαβ′, which can be integrated all over the three-dimensional space to evaluate components καβ′ and trace καα′. A computational approach to kαβ′, based on frequency-dependent electronic current densities induced by monochromatic light shining on a probe molecule, has been developed. The dependence of kαβ′ on the origin of the coordinate system has been investigated in connection with the corresponding change of καβ′. 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.

Anisotropy of the vorticity tensor as a magnetic indicator of aromaticity

The vorticity vector of the current density J^B, induced in the electron cloud of a molecule by a magnetic field B, is defined by V^B = ∇ × J^B.