Dynamics of wavepackets in molecular and nuclear physics

Peter Schuck

J. Broeckhove, Luc Lathouwers, Piet Van Leuven

Jiří J. L. Vaníček

Ehrenfest dynamics is a widely used mixed quantum--classical approach for nonadiabatic molecular dynamics, whereas thawed Gaussian wavepacket dynamics provides an efficient semiclassical description of adiabatic nuclear quantum dynamics. Here we describe thawed Gaussian Ehrenfest dynamics (TGED), which unifies and generalizes these two methods to capture both electronic nonadiabaticity and nuclear quantum effects within a single framework. The fully variational formulation of TGED is derived by applying the time-dependent variational principle to a Hartree product of electronic and Gaussian nuclear wavepackets. Replacing the effective locally quadratic molecular potential obtained from this variational treatment by alternative effective locally quadratic potentials yields an infinite family of TGED methods, of which we present several members. We analyze the limiting cases of the general formalism and show, in particular, that it reduces to conventional Ehrenfest dynamics in the classical limit for the nuclei and to thawed Gaussian wavepacket dynamics in the absence of electronic coupling. Finally, we present explicit geometric integrators for the entire family of methods and identify the conditions under which the different approximations become exact.

Foudhil Bouakline

We discuss the effect of molecular symmetry on coherent tunneling in symmetric double-well potentials whose two molecular equilibrium configurations are interconverted by nuclear permutations. This is illustrated with vibrational tunneling in ammonia molecules, electronic tunneling in the dihydrogen cation, and laser-induced rotational tunneling of homonuclear diatomics. In this contribution, we reexamine the textbook picture of coherent tunneling in such potentials, which is depicted with a wavepacket shuttling back and forth between the two potential-wells. We show that the common application of this picture to the aforementioned molecules contravenes the principle of the indistinguishability of identical particles. This conflict originates from the sole consideration of the dynamics of the tunneling-mode, connecting the double-well energy minima, and complete omission of all the remaining molecular degrees of freedom. This gives rise to double-well wavepackets that are nonsymmetric under nuclear permutations. To obey quantum statistics, we show that the double-well eigenstates composing these wavepackets must be entangled with the wavefunctions that describe all the omitted molecular modes. These wavefunctions have compensating and opposite nuclear permutation symmetry. This in turn leads to complete quenching of interference effects behind localization in one potential-well or another. Indeed, we demonstrate that the reduced density of probability of the symmetrized molecular wavefunction, where all the molecular coordinates but the tunneling-mode are integrated out, is symmetrically distributed over the two potential-wells, at all times. This applies to any multilevel wavepacket of isotropic or fully aligned symmetric double-well achiral molecules. However, in the case of coherent electronic or vibrational tunneling, fully aligned molecules may exhibit dynamical localization in the space-fixed frame, where the tunneling-mode density shuttles between the opposite directions of the alignment axis. This dynamical spatial-localization results from linear combinations of molecular states that have opposite parity. In summary, this study shows that dynamical localization of the tunneling-mode density on either of the two indistinguishable molecular equilibrium configurations of symmetric double-well achiral molecules is forbidden by quantum statistics, whereas its dynamical localization in the space-fixed frame is allowed by parity. The subtle distinction between these two types of localization has far-reaching implications in the interpretation of many ultrafast molecular dynamics experiments.

Thomas C. Weinacht

The control of atoms and molecules using coherent light fields has been a long-standing goal in chemical physics. This thesis discusses experiments which use a programmable pulse shaper to control the quantum state of electronic wavepackets in Rydberg atoms and electronic and nuclear dynamics in molecular liquids. The shape of Rydberg wavepackets was controlled by using tailored ultrafast pulses to excite a beam of cesium atoms. The quantum state of these atoms was measured using holographic techniques borrowed from optics. The experiments with molecular liquids involved the construction of an automated learning machine. A Genetic Algorithm directed the choice of shaped pulses which interacted with the molecular system inside a learning control loop. Analysis of successful pulse shapes that were found by using the GA yield insight into the systems being controlled.

Mordechai Bixon