Topological data analysis of vortices in the magnetically-induced current density in LiH molecule

A novel strategy for extracting axial (AV) and toroidal (TV) vortices in the magnetically-induced current density (MICD) in molecular systems is introduced, and its pilot application to LiH molecule is demonstrated. It exploits differences in the topologies of AV and TV cores and involves two key steps: selecting a scalar function that can describe vortex cores in MICD and its subsequent topological analysis. The scalar function of choice is Ω^B_α based on the velocity-gradient Ω method known in research on classical flows. The Topological Data Analysis (TDA) is then used to analyze the Ω^B_α scalar field. In particular, TDA robustly assigns distinct topological features of this field to different vortex types in LiH: AV to saddle-maximum separatrices which connect maxima to 2-saddles located on the domain's boundary, TV to a 1-cycle of the super-level sets of the input data. Both are extracted as the most persistent features of the topologically-simplified Ω^B_α scalar field.

Aromaticity Concepts Derived from Experiments

Aromaticity, a very important term in organic chemistry, has never been defined unambiguously. Various ways to describe it come from different phenomena that have been experimentally observed. The most important examples related to some theoretical concepts are presented here.

Current density and molecular magnetic properties

We give an overview of the molecular response to an external magnetic field perturbing quantum mechanical systems. We present state-of-the-art methods for calculating magnetically-induced current-density susceptibilities. We discuss the essence and properties of current-density susceptibilities and how molecular magnetic properties can be calculated from them. We also review the theory of spin-current densities, how relativity affects current densities and magnetic properties. An overview of the magnetic ring-current criterion for aromaticity is given, which has implications on theoretical and experimental research. The recently reported theory of antiaromaticity and how molecular symmetry affects the magnetic response are discussed and applied to closed-shell paramagnetic molecules. The topology of magnetically induced current densities and its consequences for molecular magnetic properties are also presented with twisted and toroidal molecules as examples.

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

We present SYSMOIC, a program package for the calculation of the origin-independent current density induced at first order by an external magnetic field in planar and nonplanar molecular systems. Origin independence is obtained adopting the continuous transformation of the origin of the current density method, implemented at both density functional theory (DFT) and Hartree-Fock (HF) levels. Expansion coefficients for perturbed and unperturbed molecular orbitals, over basis sets containing up to m-type Gaussian functions, can be calculated by the package itself or obtained from a Gaussian calculation. A number of different functionalities presented so far in the literature that are connected to the induced current, such as current density maps for any orientation of the inducing magnetic field, net bond current strengths, stagnation graphs, magnetic shielding densities, vorticities, and anisotropies, are now made available all together in a single multiplatform package installation.

The effect of anion complexation on the aromatic properties of aromatic and antiaromatic porphyrinoids

The effect of anion complexation on magnetically induced current densities and excitation energies of antiaromatic molecular rings has been investigated by calculations on expanded antiaromatic porphyrinoids including orangarin, rosarin, amethyrin and on a theoretically predicted strongly antiaromatic hydrocarbon ring.

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.