arXiv subjects

Raphael J. F. Berger

Publications and source records attributed to Raphael J. F. Berger.

3 recordsLinked to original sources

arXiv2025

Magnetically Induced Current Density from Numerical Positional Derivatives of Nucleus Independent Chemical Shifts

Instead of computing magneticallly induced (MI) current densities (CD) via the wave function and their quatum mechanical definition one can also use the differential form of the Ampère-Maxwell law to obtain them from spatial derivatives of the induced magnetic field. In magnetic molecular response calculations, the latter can be done by numerical derivativation of the so called ``nucleus-independent chemical shifts'' (NICS) which are avaialable to many standard quantum chemical programs. The resulting numerical MICD data is in contrast to other numerically obtained MICDs computed via the wave function route, virtually divergence-free.

physics.chem-ph↗

arXiv2024

The Quantum Mechanical Problem of a Particle on a Ring with Delta Well

The problem of a spin-free electron with mass $m$, charge $e$ confined onto a ring of radius $R_0$ and with an attractive Dirac delta potential with scaling factor (depth) $κ$ in non-relativistic theory has closed form analytical solutions. The single bound state function is of the form of a hyperbolic cosine that however contains a parameter $d>0$ which is the single positive real solution of the transcendental equation $\coth(d) = λd$ for non zero real $λ=\frac{2}{πκ}$. The energy eigenvalue of the bound state $\varepsilon=-\frac{d^2}{2π^2}\approx \frac{q e m R_0}{2 \hbar^2}$. In addition a discretly infinite set of unbounded solutions exists, formally these solutions are obtained from the terms for the bound solution by substituting $d \to i d $ yielding $\cot(d) = λd$ as characteristic equation with the corresponding set of solutions $d_k, k\in\mathbb{N}$, the respective state functions can be obtained via $\cosh(x)\overset{x \to i x}{\longrightarrow}\cos(x)$.

quant-ph↗

arXiv2019

The principle underlying antiaromaticity

Aromaticity is one of the most widely used chemical concepts. Current definitions are purely phenomenological and relate symmetry, reactive stability and the occurence of molecular diamagnetic response currents. The antithetical concept of antiaromaticity provides a connection between the contrary properties of structural instability or distortion out of higher symmetry, a small HOMO-LUMO gap, and paramagnetic response currents. We reveal the principle that is underlying antiaromaticity in showing an intimate and strict symmetry induced relation between these properties. This principle can be proven and is formulated like: First order (and related) Jahn-Teller distorted molecules out of non-isometric point groups are prone to paramagnetic current susceptibility parallel to the main axis of symmetry. We show by the exemplary cases of cyclobutadiene, cylcooctatetraene, pentalene and manganese trifluoride how this principle works and discuss this new perspective on antiaromaticity.

physics.chem-ph↗