Maximum tunneling velocities in symmetric double well potentials

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 rearrangment 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

Quantum Control on the Attosecond Time Scale

This article starts with an introductory survey of previous work on breaking and restoring the electronic structure symmetry of atoms and molecules by means of two laser pulses. Accordingly, the first pulse breaks the symmetry of the system in its ground state with irreducible representation IRREPg by exciting it to a superposition of the ground state and an excited state with different IRREPe . The superposition state is non-stationary, representing charge migration with period T in the sub- to few femtosecond time domains. The second pulse stops charge migration and restores symmetry by de-exciting the superposition state back to the ground state. Here, we present a new strategy for symmetry restoration: The second laser pulse excites the superposition state to the excited state, which has the same symmetry as the ground state, but different IRREPe . The success depends on perfect time delay between the laser pulses, with precision of few attoseconds. The new strategy is demonstrated by quantum dynamics simulation for an oriented model system, benzene

From photoelectron detachment spectra of BrHBr−, BrDBr− and IHI−, IDI− to vibrational bonding of BrMuBr and IMuI

Photoelectron detachment XLX−(0000) + hν → XLX(vib) + e − + KER (X = Br or I, L = H or D) at sufficiently low temperatures photoionizes linear dihalogen anions XLX− in the vibrational ground state (v 1 v 2 l v 3 = 0000) and prepares the neutral radicals XLX(vib) in vibrational states (vib). At the same time, part of the photon energy (hν) is converted into kinetic energy release (KER) of the electron [R. B. Metz, S. E. Bradforth, and D. M. Neumark, Adv. Chem. Phys. 81, 1 (1992)]. The process may be described approximately in terms of a Franck-Condon type transfer of the vibrational wavefunction representing XLX−(0000) from the domain close to the minimum of its potential energy surface (PES) to the domain close to the linear transition state of the PES of the neutral XLX. As a consequence, prominent peaks of the photoelectron detachment spectra (pds) correlate with the vibrational energies E XLX,vib of states XLX(vib) which are centered at linear transition state. The corresponding vibrational quantum numbers may be labeled vib = (v 1 v 2 l v 3) = (000 v 3). Accordingly, the related most prominent peaks in the pds are labeled v 3. We construct a model PES which mimics the “true” PES in the domain of transition state such that it supports vibrational states with energies E XLX,pds,000v3 close to the peaks of the pds labeled v 3 = 0, 2, and 4. Subsequently, the same model PES is also used to calculate approximate values of the energies E XMuX,0000 of the isotopomers XMuX(0000). For the heavy isotopomers XHX and XDX, it turns out that all energies E XLX,000 v 3 are above the threshold for dissociation, which means that all heavy XLX(000 v 3) with wavefunctions centered at the transition state are unstable resonances with finite lifetimes. Turning the table, bound states of the heavy XLX are van der Waals (vdW) bonded. In contrast, the energies E XMuX,0000 of the light isotopomers XMuX(0000) are below the threshold for dissociation, with wavefunctions centered at the transition state. This means that XMuX(0000) are vibrationally bonded. This implies a fundamental change of the nature of chemical bonding, from vdW bonding of the heavy XHX, XDX to vibrational bonding of XMuX. For BrMuBr, the present results derived from experimental pds of BrHBr− and BrDBr− confirm the recent discovery of vibrational bonding based on quantum chemical ab initio calculations [D. G. Fleming, J. Manz, K. Sato, and T. Takayanagi, Angew. Chem., Int. Ed. 53, 13706 (2014)]. The extension from BrLBr to ILI means the discovery of a new example of vibrational bonding. These empirical results for the vibrational bonding of IMuI, derived from the photoelectron spectra of IHI− and IDI−, are supported by ab initio simulations of the spectra and of the wavefunction representing vibrational bonding of IMuI

Electron Symmetry Breaking during Attosecond Charge Migration Induced by Laser Pulses: Point Group Analyses for Quantum Dynamics

Quantum simulations of the electron dynamics of oriented benzene and Mg-porphyrin driven by short (<10 fs) laser pulses yield electron symmetry breaking during attosecond charge migration. Nuclear motions are negligible on this time domain, i.e., the point group symmetries G = D6h and D4h of the nuclear scaffolds are conserved. At the same time, the symmetries of the one-electron densities are broken, however, to specific subgroups of G for the excited superposition states. These subgroups depend on the polarization and on the electric fields of the laser pulses. They can be determined either by inspection of the symmetry elements of the one-electron density which represents charge migration after the laser pulse, or by a new and more efficient group-theoretical approach. The results agree perfectly with each other. They suggest laser control of symmetry breaking. The choice of the target subgroup is restricted, however, by a new theorem, i.e., it must contain the symmetry group of the time-dependent electronic Hamiltonian of the oriented molecule interacting with the laser pulse(s). This theorem can also be applied to confirm or to falsify complementary suggestions of electron symmetry breaking by laser pulses

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

An elementary molecular process can be characterized by the flow of particles (i.e., electrons and nuclei) that compose the system. The flow, in turn, is quantitatively described by the flux (i.e., the time-sequence of maps of the rate of flow of particles though specified surfaces of observation) or, in more detail, by the flux density. The quantum theory of concerted electronic and nuclear fluxes (CENFs) associated with electronically adiabatic intramolecular processes is presented. In particular, it is emphasized how the electronic continuity equation can be employed to circumvent the failure of the Born–Oppenheimer approximation, which always predicts a vanishing electronic flux density (EFD). It is also shown that all CENFs accompanying coherent tunnelling between equivalent “reactant” and “product” configurations of isolated molecules are synchronous. The theory is applied to three systems of increasing complexity. The first application is to vibrating, aligned H2+(2Σg+), or vibrating and dissociating H2+(2Σg+, J = 0, M = 0). The EFD maps manifest a rich and surprising structure in this simplest of systems; for example, they show that the EFD is not necessarily synchronous with the nuclear flux density and can alternate in direction several times over the length of the molecule. The second application is to coherent tunnelling isomerization in the model inorganic system B4, in which all CENFs are synchronous. The contributions of core and valence electrons to the EFD are separately computed and it is found that core electrons flow with the nuclei, whereas the valence electrons flow obliquely to the core electrons in distinctive patterns. The third application is to the Cope rearrangement of semibullvalene, which also involves coherent tunnelling. An especially interesting discovery is that the so-called “pericyclic” electrons do not behave in the manner typically portrayed by the traditional Lewis structures with appended arrows. Indeed, it is found that only about 3 pericyclic electrons flow, in contrast to the 6 predicted by the Lewis picture. It is remarkable that the time scales of these three processes vary by 18 orders of magnitude: femtoseconds (H2+(2Σg+)); picoseconds (B4); kilosceconds (semibullvalene). It is emphasized that results presented herein are appearing in the literature for the first time

From coherent quasi-irreversible quantum dynamics towards the second law of thermodynamics: The model boron rotor B13+

The planar boron cluster B13+ provides a model to investigate the microscopic origin of the second law of thermodynamics in a small system. It is a molecular rotor with an inner wheel that rotates in an outer bearing. The cyclic reaction path of B13+ passes along thirty equivalent global minimum structures (GMi, i = 1, 2, ..., 30). The GMs are embedded in a cyclic thirty-well potential. They are separated by thirty equivalent transition states with potential barrier Vb. If the boron rotor B13+ is prepared initially in one of the thirty GMs, with energy below Vb, then it tunnels sequentially to its nearest, next-nearest etc. neighbors (520 fs per step) such that all the other GMs get populated. As a consequence, the entropy of occupying the GMs takes about 6 ps to increases from zero to a value close to the maximum value for equi-distribution. Perfect recurrences are practically not observable

From Molecular Symmetry Breaking to Symmetry Restoration by Attosecond Quantum Control

International audienc

From Molecular Symmetry Breaking to Symmetry Restoration by Attosecond Quantum Control

International audienc