CE29 - Chimie : analyse, théorie, modélisation

Quantum Dynamics of the Diffusion of Adsorbates – QDDA

Quantum Dynamics of the Diffusion of Adsorbates

The diffusion of reactive adsorbates on a catalytic substrate is an elementary step in heterogeneous catalysis. Its nature has been by 3He-spin-echo experiments. The project is to study the diffusion process from fundamental principles based on quantum mechanics in order to better understand the experimental outcomes. This study will lead to major progress in the technology of catalytic processes, essential for the world’s economy and sustainable growth.

Quantum effects during the diffusion of adsorbed particles

Heterogeneous catalysis is an essential process for the world's economy and its sustainable growth. While progress to its understanding has been made in the past decades, many elementary steps remain unresolved, such as the diffusion of the chemically reacting adsorbates on the catalytic substrate. The nature of this elementary step has been unraveled since about 10 years by high resolution 3He-spin-echo experiments. The interpretation of these experiments remains controversial. A recent theory, which is based on first principle calculations, shows that quantum effects are important above room temperature. The objectives of the present project are: 1) the investigation of the diffusion of adsorbates within a full quantum mechanical calculation with appropriate models to mimic the dense structure of levels; 2) the development of mathematical and numerical tools for these investigations; 3) the study of systems that represent quite different physical situations.<br /><br />The illustration below is a cartoon of the motion of a CO molecule adsorbed on a Cu(100) surface, to mention one example of the systems investigated. The function V(x,y) shows the calculated potential energy surface along the x and y coordinates defining the surface (left hand side). On the “top” sites, above a copper atom (right hand side) the potential energy is minimal. On a “bridge” site, between two copper atoms, the potential energy has a first barrier. On the “hollow” site, in the middle of four copper atoms, the barrier is about 3 times higher than the barrier on the “bridge” site. The different heights of the potential energy surface, which resembles a topographical surface, hamper the motion of the adsorbate along the substrate: classically, it has to jump from one stable (“top”) site to the other; quantum mechanically, it can “tunnel” through the barriers.

Observable quantities in 3He-spin-echo experiments are the dynamical structure factor (DSF) and the intermediate scattering function (ISF). Core to the project is a new computational method to evaluate the ISF from first principle calculations will be proposed. The method is based on the computation of the evolution of wave packets obtained as solutions of the time dependent Schrödinger equation with stochastic initial conditions reflecting the thermal state of the system. Particular attention is needed for the treatment of the coupling of the adsorbate’s motion with the motion of the atoms in the substrate. Both the solution of the quantum mechanical equations of motion of the adsorbates as well as the treatment of their coupling with the environment will be implemented in large computer programs devoted to the calculation of quantum dynamical quantities.

Expected milestone results are: The complete, realistic simulation of the motion of an adsorbed diatomic molecule on a metallic substrate, according to quantum mechanics, for four benchmark systems. Methods to evaluate diffusion rates from full quantum, first principle calculations of the DSF and ISF. The validation of both time independent (DSF) and time dependent methods (ISF) will be crucial for their reliability. A method to implement, with increasing degrees of freedom, the vibrational modes of the substrate atoms into the dynamics of the adsorbates’ diffusion. A method to implement non-adiabatic or phonon couplings using a system-bath treatment with stochastic operators. A reliable rationalization of experimental data in terms of characteristic dynamical properties of the systems: vibrational frequencies, diffusion barriers and lifetimes of excited adsorbate states.

In the short term, this project will very likely lead to a new procedure on how the topography of potential energy landscapes for the diffusion of adsorbates is rationalized and validated. The latter are important ingredients used in model calculations of catalytic processes that are generally applied for the development of new catalysts. Their reliable derivation from first principle, full quantum calculations will lead to a considerable reduction of ambiguities in the model calculations and hence to improved technologies in the preparation of catalytic surfaces, both under economy and sustainability aspects.

Catalyst business has a very important impact on socioeconomic factors and the sustainability of the world’s economy (estimated annual turnover of about US dollars, about people employed worldwide and potential reduction of energy consumption in chemical industry and greenhouse gases). In the long term, the accrued knowledge is therefore a true benefice for society. The clear aim to strongly focus the theoretical work on the interpretation of experimental results, in particular the helium-3 spin-echo experiments, makes this project very interesting for applied scientists working in the catalyst industry. The project is exploratory, as it establish the underpinning of a more efficient chemistry based on quantum technology for new technological applications. Chemistry supplies an essential basis for modern life, and improving the efficiency of chemical processes by their control at the microscopic level addresses two major societal issues, energy consumption and pollution. This will undoubtedly have an enormous impact on the economy as well as on society.

The project started effectively in July 2020. As per July 2021, a computer code has been created to implement the interaction of adsorbed particles with the environment and first publications documenting the progress of the research are in the submission process.

This project is a theoretical investigation of the dynamics of single molecules adsorbed on a metallic crystalline substrate. Since the pioneering work by Langmuir we know that the adsorption processes play a key role in the field of heterogeneous catalysis. The 2007 Nobel Prize of Chemistry attributed to G. Ertl for his experimental findings regarding, among others, the understanding of elementary steps in the synthesis of ammonia on iron, underlined the societal importance of this research. However, the understanding of these elementary steps remains mainly phenomenological: very few studies based on the actual quantum dynamics of molecular adsorption have been undertaken, to date, at the microscopic level. One fundamental dynamical aspect is diffusion on the substrate. This material dependent property can perhaps be most accurately assessed experimentally via helium-3 spin-echo experiments. These experiments rely on the evaluation of the so-called dynamical structure factor (DSF) and its Fourier transform, the intermediate scattering function (ISF), introduced by van Hove in 1954. The theoretical assessment of the observables related to these functions is very difficult. In the processor project DYQUMA, a pure quantum approach to calculate diffusion rates based on the DSF was successfully developed. However, serious controversies in the interpretation of experimental data persist and several questions have remained open since then, among which two major questions emerge: How do we evaluate theoretically the directly observed intermediate scattering function (ISF) from a pure quantum dynamical calculation? What is the precise role of the lifetimes of vibrationally excited adsorbates due to the coupling with phonons or electron-hole pairs?
Relevant answers to these questions will allow us to solve open controversies; they will pave the road for future research in surface science and guide the catalytic processes; they are therefore highly pertinent technologically both in the gas phase as well as in the domain of heterogeneous catalysis and surface chemistry. One general aim of this project is to open new perspectives in this field. We will concentrate on a microscopic approach, and give quantitative and rigorous insight for a given class of important systems.
The various parameters which may influence the physics of the process will be taken into account as completely as possible. In this project, the dynamics of the adsorbed atoms and molecules will be treated quantum mechanically. The proper understanding of quantum effects is strongly susceptible to carry us to new technological applications in the aforementioned fields.
The project will face two major theoretical challenges: first, we need to calculate the quantum dynamics in many dimensional spaces; the largest difficulty that arises in this respect is the very rapidly increasing density of vibrational states due to the low energies of eigenstates pertaining to frustrated translations parallel to the substrate as well as hindered rotations of the adsorbed species; since first principle calculations of potential energy surfaces in the appropriate zero-coverage limit are extremely difficult, the modeling of the single particle quantum dynamics is a formidable challenge. Secondly, even the single particle dynamics of adsorbed species cannot be treated in a fully realistic way without appropriate consideration of couplings to the quasi-continuum of electronic substrate states, of the coupling to substrate phonons and, potentially, of further couplings to electronic states of the adsorbate itself. In this project we will cope with all these challenges.

Project coordinator

Monsieur Roberto Marquardt (Institut de Chimie de Strasbourg (UMR 7177))

The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.


IC_UNISTRA Institut de Chimie de Strasbourg (UMR 7177)
LPCT Laboratoire de Physique et Chimie Théoriques
ISMO Institut des Sciences Moléculaires d'Orsay

Help of the ANR 242,599 euros
Beginning and duration of the scientific project: December 2019 - 48 Months

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