Translational Effects on Electronic and Nuclear Ring Currents

Molecular Pseudorotation in Phthalocyanines as a Tool for Magnetic Field Control at the Nanoscale

Metal phthalocyanines, a highly versatile class of aromatic, planar, macrocyclic molecules with a chelated central metal ion, are topical objects of ongoing research and particularly interesting due to their magnetic properties. However, while the current focus lies almost exclusively on spin-Zeeman-related effects, the high symmetry of the molecule and its circular shape suggests the exploitation of light-induced excitation of 2-fold degenerate vibrational states in order to generate, switch, and manipulate magnetic fields at the nanoscale. The underlying mechanism is a molecular pseudorotation that can be triggered by infrared pulses and gives rise to a quantized, small, but controllable magnetic dipole moment. We investigate the optical stimulation of vibrationally induced molecular magnetism and estimate changes in the magnetic shielding constants for confirmation by future experiments.

Probability and Flux Densities in the Center-of-Mass Frame

For an arbitrary nonstationary wave function of a nonrelativistic closed many-body system consisting of arbitrary interacting particles, the general expressions for the time-dependent one-particle probability and flux densities in the center-of-mass frame without applying Born-Oppenheimer approximation are obtained. Even the wave function for the translation is additionally introduced; it disappears in the center-of-mass frame automatically. It is shown that for the rotational ground state the time-dependent probability and flux densities of an arbitrary particle in the center-of-mass frame are isotropic. It means that the angular dependence is absent but these densities depend on radius and time. More importantly, it is shown that the angular components of the time-dependent flux density vanish. With these statements, one can calculate the radial component of the radius- and time-dependent electronic flux density within the Born-Oppenheimer approximation via the continuity equation. Application of this theory to the pulsating or exploding "quantum bubble" of the vibrating or dissociating Na₂ molecule in the rotational ground state, respectively, is found elsewhere in this issue.

Concerted Electronic and Nuclear Fluxes During Coherent Tunnelling in Asymmetric Double-Well Potentials

The quantum theory of concerted electronic and nuclear fluxes (CENFs) during coherent periodic tunnelling from reactants (R) to products (P) and back to R in molecules with asymmetric double-well potentials is developed. The results are deduced from the solution of the time-dependent Schrödinger equation as a coherent superposition of two eigenstates; here, these are the two states of the lowest tunnelling doublet. This allows the periodic time evolutions of the resulting electronic and nuclear probability densities (EPDs and NPDs) as well as the CENFs to be expressed in terms of simple sinusodial functions. These analytical results reveal various phenomena during coherent tunnelling in asymmetric double-well potentials, e.g., all EPDs and NPDs as well as all CENFs are synchronous. Distortion of the symmetric reference to a system with an asymmetric double-well potential breaks the spatial symmetry of the EPDs and NPDs, but, surprisingly, the symmetry of the CENFs is conserved. Exemplary application to the Cope rearrangement of semibullvalene shows that tunnelling of the ideal symmetric system can be suppressed by asymmetries induced by rather small external electric fields. The amplitude for the half tunnelling, half nontunnelling border is as low as 0.218 × 10(-8) V/cm. At the same time, the delocalized eigenstates of the symmetric reference, which can be regarded as Schrödinger's cat-type states representing R and P with equal probabilities, get localized at one or the other minima of the asymmetric double-well potential, representing either R or P.

Quantum theory of concerted electronic and nuclear fluxes associated with adiabatic intramolecular processes

Example of concerted electronic (right) and nuclear (left) fluxes: isomerization of B₄.