Vorticity: Simplifying the analysis of the current density

Abstract

The induced current density (J(r)) provides useful information about the electronic structure of molecules under a magnetic field (B). However, the analysis of its topology is cumbersome because of its vectorial nature. We show that its tropicity (direction of rotation) and its strength can be compressed in the triple product B ⋅ ∇ × J(r) (tpJ(r)) that is a scalar field. The topology of tpJ(r) has clear similarities to the Laplacian of the electron density. Additionally, the topology of aromatic and antiaromatic compounds is notoriously different. The vorticity of J(r) is helpful to define the circulation of the current density, C, that contrary to other methods, can be easily defined for individual rings in polycyclic molecules. This allows tpJ(r) to clearly reproduce the Clar's structure of polycyclic aromatic hydrocarbons. © 2019 Wiley Periodicals, Inc.

Program Package for the Calculation of Origin-Independent Electron Current Density and Derived Magnetic Properties in Molecular Systems

“…The vorticity of the current density is a vector defined as The second-rank vorticity tensor is analogously defined as the derivative of the components of the vorticity vector with respect to the component of the magnetic field − All of the components of the vorticity tensor can be calculated analytically by SYSMOIC at any spatial point.…”

Unveiling the Impact of Aggregation on Optical Anisotropy of Triazaacephenanthrylene Single Crystals. A Combined Quantum Crystallography and Conceptual Density Functional Theory Approach

“…Recently, it was proposed that the aromaticity of the individual rings of polycyclic compounds can be effectively evaluated with the circulation ( C ) of the magnetically induced current density J ( r ). 55 The circulation is the surface integral of triple product B ·∇ × J ( r ) (tp J ( r )), which is a scalar field that indicates the diatropic (negative) and paratropic (positive) regions in a molecule. Diatropicity has been extensively related with aromaticity, while paratropicity with antiaromaticity.…”

“…The values of those two indices were compared with the results obtained via analysis of the vorticity of the current density. The geometry of the monomer and dimer of TAAP were optimized using M06/Def2-TZVP with empirical dispersion corrections, which has proven to be adequate for vorticity studies in weakly bonded systems. , The magnetically perturbed wavefunctions were obtained using gauge-including atomic orbitals. These calculations where performed with Gaussian16 .…”

“…The magnetic field, B , is perpendicular to the molecular plane. The triple product of the current density, tp J ( r ), scalar field and the circulation, C , were calculated numerically with a set of python scripts. , These scripts use the pvpython library included in Paraview 5.2. The loop for the calculation of C is the geometric structure of the molecular ring at 1.0 bohr from the molecular plane.…”

Geometry-based circulation of local thermal current in quantum harmonic and Bose Hubbard systems

“…For example, the ring geometry provides a natural shape for persistent current induced by magnetic flux [2][3][4]. Interestingly, circulation of electrons in the form of current vortices [5][6][7][8] or chiral current [9] may emerge without an external magnetic field. A metallic ring embedded with two quantum dots and connected to external electrodes shows circulating currents [10].…”