Universality of the Fermi-level decay-length descriptor and interface effects in quantum-size-modulated chemisorption on ultrathin metal films

First-principles work on CO adsorbed on ultrathin Cu(001) films supported on fcc-Fe(001) established that the chemisorption energy oscillates with film thickness with the same periodicity as quantum-well-state crossings through the Fermi level, and proposed the vacuum decay length $\lambda$ of the film local density of states at the Fermi energy as the electronic descriptor controlling these oscillations. The result, however, was obtained for a single adsorbate/substrate system, with an idealized abrupt interface, frozen geometries, and a PBE-GGA treatment. The open problem is to establish the domain of validity of this $\lambda$ mechanism: whether $\lambda$-control of chemisorption transfers quantitatively to other chemisorbed molecules and film/substrate combinations, and how realistic interface structure, including possible Cu/Fe intermixing, modifies the quantum-well spectrum and the chemisorption-energy trend in the thinnest (3–4 monolayer) films, where the original calculations disagree with experiment.

Background

In a metal film only a few atomic layers thick, the valence electrons are confined perpendicular to the surface, and the continuous bands split into discrete subbands known as quantum-well states (QWS). As the film thickness $L$ is increased monolayer (ML) by monolayer, these subbands shift downward in energy and cross the Fermi energy $E_F$ one at a time at the surface Brillouin-zone center $\bar{\Gamma}$. Because a surface chemical bond is formed largely by electronic states near $E_F$, such quantum-size effects (QSE) make surface properties — including chemical reactivity — oscillate periodically with $L$. The landmark experiment for chemisorption was performed by Danese, Curti, and Bartynski (2004), who measured the desorption temperature of carbon monoxide (CO) from epitaxial Cu(001) films grown on fcc-Fe(001): it oscillated with film thickness, with the largest desorption temperatures coinciding with thicknesses at which a QWS crosses $E_F$ as detected by inverse photoemission (a spectroscopy in which an injected electron emits a photon, probing the unoccupied states above $E_F$). The chemisorption energy $E_{ch}$ is the total-energy gain per molecule on adsorption, and the desorption temperature is its experimental proxy.

Several electronic descriptors had been proposed for QSE-controlled reactivity in related systems: the oscillation of the density of states (DOS) at $E_F$ was invoked for the oxidation of Mg and Pb films, and for physisorption-like processes Aballe et al. (2010) argued that reactivity is controlled by the decay length $\lambda$ of the electronic local density of states (LDOS) at $E_F$ — the LDOS outside the surface decays approximately exponentially into the vacuum, $\rho(z,E_F)\propto\exp(-2z/\lambda)$, and $\lambda$ measures how far the $E_F$ states extend outward. For chemisorbed CO on Cu(001), which descriptor actually operates was not established.

Mouketo, Binggeli, and M'Passi-Mabiala (2011) addressed this with density-functional theory (DFT) using the PBE generalized-gradient-approximation exchange-correlation functional (PBE-GGA), computing $E_{ch}(L)$ for CO on free-standing and Fe-supported (5 ML of ideal, abrupt fcc-Fe(001)) Cu(001) films of 3–12 ML at coverages of 1.0 and 0.5 ML, with the slab geometry frozen at the clean-surface structure. They found: (i) $E_{ch}$ oscillates with the periodicity of the $\bar{\Gamma}$ QWS crossings through $E_F$, with maxima one ML before the crossings (at 4 and 10 ML); (ii) the DOS per atom at $E_F$ oscillates with a short 2–3 ML beating period, out of phase with $E_{ch}$, and is ruled out as the controlling descriptor; (iii) work-function oscillations and monotonic shifts of the Cu $3d$ band are also out of phase and ruled out; (iv) $\lambda$ oscillates in phase with the QWS crossings (maximum when the highest occupied QWS lies just below $E_F$) and correlates approximately linearly with $E_{ch}$ for the Fe-supported films of 5–12 ML — the basis of the $\lambda$ mechanism, in which longer-reaching $E_F$ states enhance the overlap and hybridization (donation from the CO $5\sigma$ orbital and back-donation into the unoccupied CO $2\pi^{*}$ orbital) that forms the chemisorption bond. A symmetry argument completes the picture: at $\bar{\Gamma}$ the QWS are predominantly Cu $4s$-like with about 10% $d_{\sigma}$ character and cannot couple to the CO $2\pi^{*}$; the $d_{\pi}$ component that can couple grows only at finite in-plane wave vector $k_{\parallel}$, so maximal back-donation requires a small but non-zero occupied fraction of the subband — realized one ML before the crossing. Related QSE-reactivity systems studied around the same time include the experimental quantum oscillation of the oxidation rate of Pb films (Ma et al. 2007) and its theory (Yang et al. 2008; Hu et al. 2010), and first-principles decay lengths of Pb films (Li et al. 2011), none of which involve a chemisorption-energy descriptor test.

The source study itself acknowledges its limits: the substrate is modeled as an ideal abrupt ferromagnetic fcc-Fe(001) slab, the calculation differs from experiment exactly at the thinnest films (a calculated $E_{ch}$ maximum at 4 ML versus an experimental decrease from 5 to 3 ML, which the authors attribute to unmodeled interface details such as atomic intermixing at the Cu/Fe interface), geometries are frozen, and the PBE-GGA treatment misestimates the CO molecular gap (a GGA+$U$ check with $U_{CO}=0.75$ eV left the thickness variations unchanged within 0.1 meV, but absolute energies shift). Whether the $\lambda$ mechanism operates beyond this one system remains an open question.

Problem Statement

Establish the domain of validity of the $\lambda$ mechanism for quantum-size-modulated chemisorption proposed by Mouketo, Binggeli, and M'Passi-Mabiala (2011) for CO on Fe-supported Cu(001) films (3–12 ML).

(1) Transferability of the descriptor. Determine whether the approximately linear correlation between the vacuum decay length $\lambda(L)$ of the film LDOS at $E_F$ and the chemisorption energy $E_{ch}(L)$ — established only for CO on Fe-supported Cu(001) films of 5–12 ML — holds for other chemisorbed molecules and other film/substrate metal combinations, or is system-specific. For this purpose a representative set of these new systems suffices to establish the domain of validity; a class of systems is fixed by the adsorbate's frontier-orbital character and by the film/substrate quantum-well-state orbital character, whose values are, along the adsorbate axis: σ donation only, σ donation combined with π back-donation (the class of CO), and closed-shell physisorption; and, along the film/substrate axis: a film on a d-band-metal substrate, a film on an s–p-band-metal substrate, and a free-standing film. The set must contain at least one system for every combination of an adsorbate class and a film/substrate class, all beyond CO on Fe-supported Cu(001). Where it holds, characterize the phase relation between $E_{ch}$ extrema and the $\bar{\Gamma}$ quantum-well-state crossings through $E_F$; where it fails, identify which electronic descriptor (state-specific level alignment between quantum-well states and the molecular frontier orbitals, DOS at $E_F$, work-function oscillations, or band shifts) governs the thickness dependence in each class of systems.

(2) The thinnest-film regime. Quantify how realistic Cu/Fe(001) interface structure — in particular possible atomic intermixing at the interface, as opposed to the ideal abrupt 5-ML fcc-Fe(001) substrate of the source calculations — modifies the quantum-well spectrum and the electronic boundary conditions, and hence the chemisorption energies at 3–4 ML; specifically, whether interface realism reconciles the calculated local maximum of $E_{ch}$ at 4 ML with the experimentally observed decrease of the CO desorption energy from 5 to 3 ML.

Both parts serve one objective — delimiting where and why the $\lambda$ mechanism controls quantum-size-modulated chemisorption.

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