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If the Born-Oppenheimer approximation is invoked for the description of chemical reactions, the electron density rearranges following the motion of the nuclei. Even though this approach is central to theoretical chemistry, the explicit time dependence of the electron density is rarely studied, especially if the nuclei are treated quantum mechanically. In this article, we model the motion of benzene along the Kekulé vibrational coordinate to simulate the nuclear dynamics and electron density dynamics in the electronic ground state. Details of the change of core, valence, and π electrons are determined and analyzed. We show how the pictures anticipated by drawing Lewis structures of the rearrangement correlate with the time-dependent quantum description of the process.

We consider coherent tunneling of one-dimensional model systems in non-cyclic or cyclic symmetric double well potentials. Generic potentials are constructed which allow for analytical estimates of the quantum dynamics in the non-relativistic deep tunneling regime, in terms of the tunneling distance, barrier height and mass (or moment of inertia). For cyclic systems, the results may be scaled to agree well with periodic potentials for which semi-analytical results in terms of Mathieu functions exist. Starting from a wavepacket which is initially localized in one of the potential wells, the subsequent periodic tunneling is associated with tunneling velocities. These velocities (or angular velocities) are evaluated as the ratio of the flux densities versus the probability densities. The maximum velocities are found under the top of the barrier where they scale as the square root of the ratio of barrier height and mass (or moment of inertia), independent of the tunneling distance. They are applied exemplarily to several prototypical molecular models of non-cyclic and cyclic tunneling, including ammonia inversion, Cope rearrangement of semibullvalene, torsions of molecular fragments, and rotational tunneling in strong laser fields. Typical maximum velocities and angular velocities are in the order of a few km/s and from 10 to 100 THz for our non-cyclic and cyclic systems, respectively, much faster than time-averaged velocities. Even for the more extreme case of an electron tunneling through a barrier of height of one Hartree, the velocity is only about one percent of the speed of light. Estimates of the corresponding time scales for passing through the narrow domain just below the potential barrier are in the domain from 2 to 40 fs, much shorter than the tunneling times. [ABSTRACT FROM AUTHOR]

Coherent tunnelling in molecular systems with cyclic and non-cyclic symmetric double well potentials may proceed with similar nuclear densities, but with entirely different flux densities. For sufficiently high potential barriers, the nuclear densities may even become indistinguishable, whereas the patterns of the flux densities at a given time remain pincer-motion type for the cyclic systems, but unidirectional for the non-cyclic one. This effect is traced back to symmetry breaking of the cyclic to the non-cyclic model. Accordingly, nuclear flux densities are much more sensitive to symmetry breaking than nuclear densities. For a proof of principle, the phenomenon is demonstrated by means of three one-dimensional models. The cyclic model I represents torsion in oriented B2Cl2F2, the non-cyclic model II is constructed from I by symmetry breaking and the non-cyclic model III represents tunnelling by inversion of oriented NH3. [ABSTRACT FROM AUTHOR]