Yonggang Yang

Vibrating H2+(2Σg+, JM = 00) Ion as a Pulsating Quantum Bubble in the Laboratory Frame

We present quantum dynamics simulations of the concerted nuclear and electronic densities and flux densities of the vibrating H2(+) ion with quantum numbers (2)Σg(+), JM = 00 corresponding to the electronic and rotational ground state, in the laboratory frame. The underlying theory is derived using the nonrelativistic and Born–Oppenheimer approximations. It is well-known that the nuclear density of the nonrotating ion (JM = 00) is isotropic. We show that the electronic density is isotropic as well, confirming intuition. As a consequence, the nuclear and electronic flux densities have radial symmetry. They are related to the corresponding densities by radial continuity equations with proper boundary conditions. The time evolutions of all four observables, i.e., the nuclear and electronic densities and flux densities, are illustrated by means of characteristic snapshots. As an example, we consider the scenario with initial condition corresponding to preparation of H2(+) by near-resonant weak field one-photon-photoionization of the H2 molecule in its ground state, (1)Σg(+), vJM = 000. Accordingly, the vibrating, nonrotating H2(+) ion appears as pulsating quantum bubble in the laboratory frame, quite different from traditional considerations of vibrating H2+ in the molecular frame, or of the familiar alternative scenario of aligned vibrating H2(+) in the laboratory frame.

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 generic results may be scaled such that they agree well with periodic potentials for which semi-analytical results in terms of Mathieu functions exist. nStarting from a wavepacket which is initially localized in one of the potential wells, the subsequent periodic tunneling is associated with tunneling velocities. nThese velocities (or angular velocities) are evaluated as the ratio of the flux densities versus the probability densities. nThe 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. nThey 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. nTypical values of the 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. 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 most difficult narrow domain (about one tenth of the distance between the potential minima) just below the potential barrier are in the domain from 2 to 40 fs, much shorter than the tunneling times.

Nuclear fluxes during coherent tunnelling in asymmetric double well potentials

Previous results for nuclear fluxes during coherent tunnelling of molecules with symmetric double well potentials are extended to fluxes in asymmetric double well potentials. The theory is derived using the two-state approximation (TSA). The symmetric system serves as a reference. As an example, we consider the one-dimensional model of the tunnelling inversion of oriented ammonia, with semiclassical dipole coupling to an electric field. The tunnelling splitting increases with the dipole coupling by a factor The tunnelling time decreases by The nuclear density appears as the sum of two parts: The tunnelling part decreases as times the density of the symmetric reference, whereas the non-tunnelling part is the initial density times Likewise, the nuclear flux decreases by with essentially the same shape as for the symmetric reference, with maximum value at the potential barrier. Coherent nuclear tunnellings starting from the upper or lower wells of the asymmetric potential are equivalent. The results are universal, in the frame of the TSA, hence they allow straightforward extrapolations from one system to others. This is demonstrated by the prediction of isotope effects for five isotopomers of ammonia.

Reconstruction of the electronic flux during adiabatic attosecond charge migration in HCCI

ABSTRACT Recently, it was shown that a well-designed laser pulse may prepare an oriented linear molecular ion in a specific superposition state of the electronic ground (g) and first excited (e) states, with different amplitudes and non-zero phases. The reconstruction of the initial state, with time resolution of 100 attoseconds (as), yields the subsequent charge migration that proceeds adiabatically, on the attosecond time scale (AACM). We develop the theory for the time evolutions of the axial density and the flux of the electrons, during AACM. The flux is obtained by simple scaling and time-shifting the results for the ‘reference’ scenario with equal amplitudes and zero phases. Application to the system HCCI+ confirms periodic AACM of a rather small number (0.663) of valence electrons, from the acetylenic moiety to the domain of the iodine, and back, with period = 1.85 fs. The underlying axial electronic flux is always unidirectional, with maximum absolute value at the border between the acetylenic moiety and the domain of the iodine, close to the local minimum of the axial density of the valence electrons and to its zero time derivative. The theoretical results imply new challenges for experiment, e.g. one should apply optimal control to steer AACM with maximum electronic flux, and one should investigate its initiation with time resolution below 100 as.

Generation of electronic flux during the femtosecond laser pulse tailored to induce adiabatic attosecond charge migration in

Adiabatic attosecond charge migration (AACM) in a linear molecule or cation such as means that the system has been prepared in a superposition state e.g. of the electronic ground and first excited states, corresponding to a surplus of density of valence electrons on one side which is compensated by a deficit of electron density on the other side. Subsequently, the surplus and deficit interchange such that the surplus of electron density migrates from its initial site to the opposite site, and back, periodically. The migration proceeds adiabatically on the attosecond time domain, i.e. without diabatic transitions between eigenstates. It is associated with electronic flux that mediates the charge migration. Here, we tailor a femtosecond laser pulse such that it induces AACM in the oriented model , with maximum electronic flux. The case study shows that the flux is generated already during the laser pulse, suggesting equivalent processes during laser initiations of AACM in many or all other systems. The results are obtained by means of quantum dynamics simulation.

Laser Sculpting of Atomic sp, sp2, and sp3 Hybrid Orbitals

Atomic sp, sp(2) , and sp(3) hybrid orbitals were introduced by Linus Pauling to explain the nature of the chemical bond. Quantum dynamics simulations show that they can be sculpted by means of a selective series of coherent laser pulses, starting from the 1s orbital of the hydrogen atom. Laser hybridization generates atoms with state-selective electric dipoles, opening up new possibilities for the study of chemical reaction dynamics and heterogeneous catalysis.

Communication: Electronic flux induced by crossing the transition state

We present a new effect of chemical reactions, e.g., isomerizations, that occurs when the reactants pass along the transition state, on the way to products. It is based on the well-known fact that at the transition state, the electronic structure of one isomer changes to the other. We discover that this switch of electronic structure causes a strong electronic flux that is well distinguishable from the usual flux of electrons that travel with the nuclei. As a simple but clear example, the effect is demonstrated here for bond length isomerization of Na2 (21Σu+), with adiabatic crossing the barrier between the inner and outer wells of the double minimum potential that support different Rydberg and ionic type electronic structures, respectively.

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.