Peter Saalfrank

Theory of photoinduced surface reactions of admolecules

The absorption of photons by an adsorbate/substrate complex may induce a wide range of physical and chemical processes, such as desorption, dissociation and reactions. Although several of these processes have analogs in the gas phase, the presence of the surface opens new reaction pathways that are not available in the gas phase. These unique pathways can be used to control reactivity, product selectivity and yield, or to explore new reactions. Stimulated by the surge in experimental studies of surface photochemistry, various theoretical models have been recently developed to elucidate observations and explore new opportunities. In this review, we survey recent advances in the theoretical characterization of photoinduced chemical and physical processes occurring on solid surfaces. Our discussions are focused on two prototypical processes. The adsorbate photodissociation on insulator surfaces provides an ideal probe of the nonelectronic interaction with the substrate. Photochemical processes on conductors, on the other hand, highlight the excitation and relaxation processes induced by substrate hot carriers. The issues addressed here include excitation and relaxation mechanisms, the role played by internal modes of the adsorbate and energy transfer between the admolecule and the substrate. Both classical and quantum models are used in describing these processes.

Quantum dynamics of bond breaking in a dissipative environment: Indirect and direct photodesorption of neutrals from metals

The dynamics of uv/visible laser‐induced nonthermal desorption of neutral molecules from metal surfaces are studied by Liouville–von Neumann equations for quantum open systems. A one‐dimensional, two‐state Gadzuk–Antoniewicz model is adopted, representative for NO/Pt(111). Electronic quenching due to coupling of the adsorbate negative ion resonance to the metal electrons is treated within the Lindblad dynamical semigroup approach. Both indirect (hot‐electron mediated) and hypothetical direct (dipole) excitation processes are considered. For the indirect pathways, DIET (single‐excitation) and DIMET (multiple‐excitation) limits are studied using one‐ and double‐dissipative channel models, respectively. To reproduce experimental desorption yields and desorbate translational energies, we estimate the quenching lifetime for NO/Pt(111) to be less than 5 fs. We also extend previous quantum treatments of photodesorption processes to the case of coordinate‐dependent quenching rates. Further, the characteristic sca...

Density matrix description of laser-induced hot electron mediated photodesorption of NO from Pt(111)

Abstract Based on the numerical solution of the Liouville-von Neumann equation for dissipative systems, the photodesorption dynamics of NO/Pt(111) are studied. Dissipative terms are used to describe the quenching of electronically excited states on the metal, electronic dephasing and the indirect (hot-electron mediated) excitation processes in the DIMET and DIET limits. Norm and energy flow, desorption probabilities and density time-of-flight spectra are computed.

Stochastic wave packet vs. direct density matrix solution of Liouville-von Neumann equations for photodesorption problems

Abstract The performance of stochastic wave packet approaches is contrasted with a direct method to numerically solve quantum open system Liouville-von Neumann equations for photodesorption problems. As a test case a simple one-dimensional two-state state model representative for NO/Pt(111) is adopted. Both desorption induced by electronic transitions (DIET) treated by a single-dissipative channel model, and desorption induced by multiple electronic transitions (DIMET) treated by a double-dissipative channel model, are considered. It is found that stochastic wave packets are a memory-saving alternative to direct matrix propagation schemes. However, if statistically rare events as for example the bond breaking in NO/Pt(111) are of interest, the former converges only slowly to the exact results. We also find that - in the case of coordinate-independent rates - Gadzuks “jumping wave packet and weighted average” procedure frequently employed to describe DIET dynamics, is a rapidly converging variant of the stochastic wave packet approach, and therefore rigorously equivalent to the exact solution of a Liouville-von Neumann equation. The usual stochastic (Monte Carlo) wave packet approach, however, is more generally applicable, and allows for example to quantify the notion of “multiple” in DIMET processes.

Surface oscillator models for dissociative sticking of molecular hydrogen at non-rigid surfaces

Effects of surface atom motion on the dissociation dynamics of hydrogen at a copper model surface are studied using time-dependent quantum dynamics, the (ordinary) surface oscillator (SO) model of Harris et al., and a modified surface oscillator (MSO) model with a microscopically motivated molecule-surface coupling. For both models the dependence of zero-coverage dissociative sticking probabilities on (1) the Einstein oscillator frequency, (2) on anharmonicities of the surface vibrations and (3) on isotopomer masses, is studied. The unmodified SO model predicts an almost perfect insensitivity on the surface oscillator frequency which explains, therefore, the well-known good agreement with the surface mass model of Luntz and Harris. In contrast, the MSO model depends on the oscillator frequency and seems more realistic if applied to solids with a rapidly varying frequency spectrum. A further qualitative difference between the SO and the MSO models is an increase (relative to the rigid-surface case) of the dissociative sticking probability at a given impact energy predicted by the latter. The SO model predicts the opposite. This is explained by the observation that in the MSO case, low-barrier reaction paths become available during surface atom motion. In contrast in the SO model the barrier remains stiff, and the loss of relative velocity between the colliding partners is dominant. Anharmonicities in the lattice vibrations are found to have negligible effects within both models. Isotopic substitution of H with D and T, leads to an expected increase of the magnitude of surface-related corrections. It is finally shown that the MSO approach accounts in a way similar to the SO model, for the experimentally observed broadening of the sticking curve with increasing surface temperature.

Photodesorption of neutrals from metal surfaces: a wave packet study

Abstract By solving the time-dependent Schrodinger equation for representative wave packets, the desorption dynamics of neutrals from metal surfaces following photoexcitation is studied. Computational parameters are chosen to resemble NO/Pt(111). Three different one-dimensional models of increasing complexity are employed to elucidate (a) basic dynamical features, (b) the role of dissipative boundary conditions and (c) non-phenomenological quenching rates. Among the computed quantities are desorption probabilities, density and flux time-of-flight spectra, kinetic energies of the desorbing particles, and “snapshots” of the wave packets in configuration and momentum space. Besides others, effects of the initial vibrational excitation of the molecule-surface bond by temperature or by IR laser pulses, and of coordinate-dependent resonance lifetimes are discussed.

Theory of laser‐induced desorption of ammonia from Cu(111): State‐resolved dynamics, isotope effects, and selective surface photochemistry

A two‐dimensional, two‐state model is used to model the UV‐laser‐induced photodesorption dynamics of NH3 and ND3 from Cu(111) by solving the nuclear time‐dependent Schrodinger equation. By projecting the asymptotic wave functions on the asymptotic (‘‘umbrella’’) eigenstates of NH3/ND3, we find that the molecules leave the surface vibrationally hot, in agreement with experimental data. Within individual asymptotic tunneling doublets, however, the desorbates are clearly non‐Boltzmann with molecules of ‘‘gerade’’ symmetry desorbing with increased probability. Our study correlates this parity selection with details of the electronic ground state potential energy surface. An experimentally observed strong isotope effect in the desorption yields for the different isotopomers is traced back mainly to differences between the vibrational frequencies of the ‘‘umbrella’’ mode, in accord with earlier, classical models. Additionally, small tunneling and moderate zero‐point contributions are observed. Finally, the poss...

Faber and Newton polynomial integrators for open-system density matrix propagation

Two polynomial expansions of the time-evolution superoperator to directly integrate Markovian Liouville–von Neumann (LvN) equations for quantum open systems, namely the Newton interpolation and the Faber approximation, are presented and critically compared. Details on the numerical implementation including error control, and on the performance of either method are given. In a first physical application, a damped harmonic oscillator is considered. Then, the Faber approximation is applied to compute a condensed phase absorption spectrum, for which a semianalytical expression is derived. Finally, even more general applications are discussed. In all applications considered here it is found that both the Newton and Faber integrators are fast, general, stable, and accurate.

Vibrationally excited products after the photodesorption of NO from Pt(111): a two-mode open-system density matrix approach

Abstract The experimentally observed vibrational excitation of NO molecules photodesorbing from a Pt(111) surface is investigated numerically with the help of open-system density matrix theory. We extend Gadzuks jumping wave packet model to treat DIET processes (desorption induced by electronic transitions, single-excitation limit) which is equivalent to a one-channel open system Liouville-von Neumann equation with coordinate-independent quenching, to cases when the electronic relaxation becomes coordinate-dependent. This allows for a more realistic but still economic and, hence, systematic study of DIET within a two-state, two-degrees of freedom model. Adopting “reasonable” Antoniewicz-type model potentials, we find that the experimental observations can semi-quantitatively be rationalized if an electronic quenching rate decreasing with increasing Nue5f8O separation, is assumed. Preliminary two-mode DIMET simulations (desorption induced by multiple electronic transitions, multiple-excitation limit) within a stochastic wave packet approach are also presented.

Atomic-scale chemistry: Desorption of ammonia from Cu 111 induced by tunneling electrons

Abstract We report on excitation experiments on individual ammonia molecules adsorbed on Cu(111) using a low-temperature scanning tunneling microscope. Multiple electronic excitation of the ammonia–substrate bond can lead to the desorption of molecules from the substrate and their transfer to the STM tip apex. The dependency of the desorption yield on the tunneling current at different biases shows that the order of the desorption process correlates directly with the minimum number of electrons necessary to overcome the binding energy. In contrast to previous experiments, excitation with either polarity, i.e., electron and hole attachment, can cause desorption. Hartree–Fock calculations allow us to deduce from spectroscopical data that the desorption process is mediated by an ammonia modified Cuxa04s state near the Fermi level.