Research in Theoretical Photochemistry

The physics leading to photoinduced desorption is believed to be understood on a qualitative level [2]: the absorption of a photon electronically excites the admolecule, either directly or indirectly. As a result of the change in electronic structure, the molecule no longer finds itself in an equilibrium position relative to the surface and hence begins to move. The dynamics is initially determined by the topology of the excited-state potential-energy surface that the equilibrium wave function is projected onto, until after the lifetime of the excited state the wave function falls back onto the ground-state potential-energy surfaces. It continues to propagate, eventually leading to desorption if the accumulated kinetic energy is sufficient to overcome the energy barrier. Dissociation and catalytic reactions are other examples of the very rich spectrum of physical and chemical processes that may result from the absorption of a photon. It is not possible to predict the dynamics without a detailed knowledge of the topology of the relevant potential-energy surfaces.

A quantitative theory of photochemical processes requires two independent ingredients: the ability to calculate ab initio potential-energy surfaces and lifetimes as well as algorithms for realistic wave-function propagation, including the transition between the ground state and excited states. Until now most theoretical studies have concentrated on the second point. Simulations based on the time-dependent Schrödinger equation or the Liouville-von Neumann equation, which includes dissipative terms, have thus reached a high degree of sophistication [2], while the potential-energy surfaces remained largely empirical. Significant further progress in theoretical photochemistry therefore depends on the availability of ab initio potential-energy surfaces.

The Theory Department of the Fritz-Haber-Institut has been at the forefront of ab initio investigations of surface reaction dynamics since the first calculation of a six-dimensional potential-energy surface for the dissociative adsorption of hydrogen on Pd(100) [3]. Since then similar studies have been performed for a variety of substrates, notably the Si(100) surface [4,5,6], the Pd(100) surface [3,7] and several other transition metals [7]. As the dissociative adsorption and the desorption of hydrogen considered so far are adiabatic processes involving only the electronic ground state, density-functional theory was used to calculate the potential-energy surfaces. The FHImd package developed at the Fritz-Haber-Institut is a very efficient plane-wave code for such calculations. However, due to the inherent limitations of density-functional theory this method cannot be employed to investigate the excited states that are crucial for the dynamics of photoinduced processes.

The first ab initio potential-energy surfaces for excited states of NO/NiO(100) were recently calculated at the Fritz-Haber-Institut using the configuration-interaction method and a small embedded cluster to represent the substrate [8]. However, this approach is not suitable for semiconductor surfaces due to the occurrence of delocalized electronic states [6], so that in this case we instead use supercell techniques. The calculation involves two steps: first the ground-state potential-energy surface is calculated using density-functional theory as in our earlier studies. The relative excitation energies are then obtained from many-body perturbation theory. In particular, we use the GW approximation for the electronic self-energy [9] to calculate individual quasielectron and quasihole excitations, which must afterwards be correlated. Our GW code is based on the recently introduced space-time method [10] for the evaluation of the self-energy operator.

As part of its research activities in photochemistry the Theory Department, together with six European partner institutes, participates in the Research Training Network Nanoscale Photon Absorption and Spectroscopy with Electrons (NANOPHASE), which is funded by the European Commission since 2000. The overall topic of the network is the theory of nanometre-scale structures - atomic clusters, quantum dots on surfaces or embedded in materials, quantum wires, and molecules adsorbed on surfaces - and the spectroscopic processes that can be used to characterize those structures, their electronic and optical properties, and their growth.

The Theory Department further maintains a formal collaboration with the group of Professor Rex W. Godby at the University of York with the aim of developing an efficient GW code for the self-energy of large systems. This collaboration is financially supported by the Deutscher Akademischer Austauschdienst and the British Council since 1999 under the scheme British-German Academic Research Collaboration (ARC).

References

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[10] M. M. Rieger, L. Steinbeck, I. D. White, H. N. Rojas and R. W. Godby, Comput. Phys. Commun. 117, 211 (1999), cond-mat/9805246; L. Steinbeck, A. Rubio, L. Reining, M. Torrent, I. D. White and R. W. Godby, Comput. Phys. Commun. 125, 105 (2000), cond-mat/9908372.