Research

Quantum Theory of Reaction Dynamics

The application of physics with the help of mathematics and informatics to explain chemical phenomena: that is Theoretical Chemistry. It describes properties and phenomena of matter -- from simple gas molecules to complex solids. It includes the quantum chemistry of molecular systems, quantum reaction dynamics and the theory of interactions between molecules and electromagnetic fields. The objective is always to explain and predict experimental observations, and for this purpose the continual development of theoretical methods is necessary.

Our esearch priority is the theory of femtosecond chemistry, which is concerned with describing and controlling elementary chemical reactions in the femtosecond range (1 fs = 10-15 s). This is the time scale on which chemical bonds form and break. By using selective excitation, in particular ultrashort laser pulses, it is possible to control reactions in such a way that they result in a specific product. We simulate such processes by means of wave packets that describe the time evolution of bond lengths and angles. Produced by laser pulses, these wave packets move on the potential energy surfaces.

The simulation and control of reactions of this nature requires a combination of methods used in quantum chemistry, quantum reaction dynamics and laser pulse optimization. Applications include the separation of nuclear spin isomers, controlled reactions in solids and the simulation of light-driven molecular rotors -- a process that points in the direction of molecular engineering. Recently we have also extended these concepts to investigate concerted electronic and nuclear fluxes during chemical reactions and to control the electron movement, for instance, the induction of electronic ring currents. As electrons move a thousand times faster than atomic nuclei, the laser pulses must be 1000 times shorter. This requirement takes us into the uncharted territory of attosecond chemistry (1 as = 10-18 s).

Selected new publications (with videos)

H.-C. Hege, J. Manz, F. Marquardt, B. Paulus, A. Schild
Electron flux during pericyclic reactions in the tunneling limit: Quantum simulation for Cyclooctatetraene
in Festschrift H. Köppel, Chem. Phys., in press (2010)

Abstract
Pericyclic rearrangement of cyclooctatetraene (COT) proceeds from equivalent sets of two reactants to two products. In the ideal limit of coherent tunneling, these reactants and products may tunnel to each other by ring inversions and by double bond shifting (DBS). We derive simple cosinusoidal or sinusoidal time evolutions of the bond-to-bond electron fluxes and yields during DBS, for the tunneling scenario. These overall yields and fluxes may be decomposed into various contributions for electrons in so called pericyclic, other valence, and core orbitals. Pericyclic orbitals are defined as the subset of valence orbitals which describe the changes of Lewis structures during the pericyclic reaction. The quantum dynamical results are compared with the traditional scheme of fluxes of electrons in pericyclic orbitals, as provided by arrows in Lewis structures.

Animations
Example dynamics of a planar model of COT. Notice that the ground state of the molecule is tub-shaped, and the movie represents only a test calculation. The pericyclic orbitals are represented as yellow isosurface while the total electron density is shown in green/blue with different isovalues.
COT movie


A. Accardi, I. Barth, O. Kühn, J. Manz
From Synchronous to Sequential Double Proton Transfer: Quantum Dynamics Simulations for the Model Porphine
in Festschrift K. Müller-Dethlefs, J. Phys. Chem. A, in press (2010)

Abstract
Quantum dynamics simulations of double proton transfer (DPT) in the model porphine, starting from a non-equilibrium initial state, demonstrate that a switch from synchronous (or concerted) to sequential (or stepwise or successive) breaking and making of two bonds is possible. For this proof of principle, we employ the simple model of Smedarchina, Z.; Siebrand, W.; Fernandez-Ramos, A. J. Chem. Phys. 2007, 127, 174513, with reasonable definition for the domains D for the reactant R, the product P, the saddle point SP2 which is crossed during synchronous DPT, and two intermediates I = I1 + I2 for two alternative routes of sequential DPT. The wavepacket dynamics is analyzed in terms of various properties, from qualitative conclusions based on the patterns of the densities and flux densities, till quantitative results for the time evolutions of the populations or probabilities PD(t) of the domains D = R, P, SP2, and I, and the associated net fluxes FD(t) as well as the domain-to-domain (DTD) fluxes FD1,D2(t) between neighboring domains D1 and D2. Accordingly, the initial synchronous mechanism of the first forward reaction is due to the directions of various momenta, which are imposed on the wavepacket by the L-shaped part of the steep repulsive wall of the potential energy surface (PES), close to the minimum for the reactant. At the same time, these momenta cause initial squeezing followed by rapid dispersion of the representative wavepacket. The switch from the synchronous to sequential mechanism is called indirect, because it is mediated by two effects: First, the wavepacket dispersion. Second, relief reflections of the broadened wavepacket from wide regions of the inverse L-shaped steep repulsive wall of the PES close to the minimum for the product, preferably to the domains I = I1 + I2 for the sequential DPT during the first back reaction, and also during the second forward reaction, etc. Our analysis also discovers a variety of minor effects, such as direct switch of the mechanisms, as well as damped oscillations in the net fluxes and populations due to compensations of partially overlapping DTD fluxes.

Animations
The 2D and 3D animations for density and flux density dynamics of the wavefunction representing double proton transfer in the model porphine, starting from the initial state:
2D animation, 3D animation
Rev.: 04-Aug-2010